###### Advertisements

###### Advertisements

If the photon of the wavelength 150 pm strikes an atom and one of its inner bound electrons is ejected out with a velocity of 1.5 × 10^{7} ms^{–1}, calculate the energy with which it is bound to the nucleus.

###### Advertisements

#### Solution 1

Energy of incident photon (E) is given by,

`E = ("hc")/lambda`

`= ((6.626xx10^(-34) " Js")(3.0 xx 10^8 " ms"^(-1)))/(150xx10^(-12) " m")`

`= 1.3252 xx 10^(-15)` J

`= 13.252 xx 20^(-16)` J

Energy of the electron ejected (K.E)

`= 1/2 "m"_"e""v"^2`

`=1/2(9.10939xx10^(-31) " kg")(1.5 xx 10^7 " ms"^(-1))^2`

= 10.2480 × 10^{–17 }J

= 1.025 × 10^{–16} J

Hence, the energy with which the electron is bound to the nucleus can be obtained as:

= E – K.E

= 13.252 × 10^{–16} J – 1.025 × 10^{–16} J

= 12.227 × 10^{–16} J

`= (12.227xx10^(-16))/(1.602xx10^(-19))` eV

`= 7.6 xx 10^3` eV

`(5lambda_0 - 2000)/(4lambda_0 - 20000) = (5.35/2.55)^2 = 28.6225/6.5025`

`(5lambda_0 - 2000)/(4lambda_0- 2000) = 4.40177`

`17.6070lambda_0 - 5lambda_0 = 8803.537- 2000`

`lambda_0 = (6805.537)/12.607`

`lambda_0 = 539.8 "nm"`

`lamda_0 = 540 "nm"`

#### Solution 2

Energy of the incident photon= hc/λ = (6.626×10^{-34 }Js×3.0×10^{8 }ms^{-1})/(150×10^{-12}m) = 13.25×10^{-16 }J

Energy of the electron ejected = 1/2 mv^{2 }= 1/2×(9.11×10^{-31}kg)×(1.5×10^{7}ms^{-1})^{2 }= 1.025×10^{-16 }J

Energy with which the electron was bound to the nucleus = 13.25×10^{-16 }J - 1.025×10^{-16 }J

= 12.225×10^{-16 }J = 12.225×10^{-16}/1.602×10^{-19 }eV = 7.63×10^{3 }eV

#### APPEARS IN

#### RELATED QUESTIONS

An electron is orbiting in 5^{th} Bohr orbit. Calculate ionisation energy for this atom, if the ground state energy is -13.6 eV.

Obtain an expression for the radius of Bohr orbit for H-atom.

State Bohr’s third postulate for hydrogen (H2) atom. Derive Bohr’s formula for the wave number. Obtain expressions for longest and shortest wavelength of spectral lines in ultraviolet region for hydrogen atom

Calculate the radius of second Bohr orbit in hydrogen atom from the given data.

Mass of electron = 9.1 x 10^{-31}kg

Charge on the electron = 1.6 x 10^{-19} C

Planck’s constant = 6.63 x 10^{-34} J-s.

Permittivity of free space = 8.85 x 10^{-12} C^{2}/Nm^{2}

Find the frequency of revolution of an electron in Bohr’s 2nd orbit; if the radius and speed of electron in that orbit is 2.14 × 10^{-10} m and 1.09 × 10^{6} m/s respectively. [π= 3.142]

What is the maximum number of emission lines when the excited electron of an H atom in n = 6 drops to the ground state?

Draw a neat, labelled energy level diagram for H atom showing the transitions. Explain the series of spectral lines for H atom, whose fixed inner orbit numbers are 3 and 4 respectively.

Explain, giving reasons, which of the following sets of quantum numbers are not possible.

(a) n = 0, l = 0, ml = 0, ms = + ½

(b) n = 1, l = 0, ml = 0, ms = – ½

(c) n = 1, l = 1, ml = 0, ms = + ½

(d) n = 2, l = 1, ml = 0, ms = – ½

(e) n = 3, l = 3, ml = –3, ms = + ½

(f) n = 3, l = 1, ml = 0, ms = + ½

Calculate the energy required for the process

\[\ce{He^+_{(g)} -> He^{2+}_{(g)} + e^-}\]

The ionization energy for the H atom in the ground state is 2.18 ×10^{–18} J atom^{–1}

Lifetimes of the molecules in the excited states are often measured by using pulsed radiation source of duration nearly in the nanosecond range. If the radiation source has a duration of 2 ns and the number of photons emitted during the pulse source is 2.5 × 10^{15}, calculate the energy of the source.

The longest wavelength doublet absorption transition is observed at 589 and 589.6 nm. Calculate the frequency of each transition and energy difference between two excited states.

The ratio of kinetic energy of an electron in Bohr’s orbit to its total energy in the same orbit is

(A) – 1

(B) 2

(C) 1/2

(D) – 0.5

In Bohr’s model of the hydrogen atom, the radius of the first orbit of an electron is r_{0} . Then, the radius of the third orbit is:

a) `r_0/9`

b) `r_0`

c) `3r_0`

d) `9r_0`

if `E_p` and `E_k` represent potential energy and kinetic energy respectively, of an orbital electron, then, according to B9hr's theory:

a)`E_k = -E_p"/"2`

b) `E_k = -E_p`

c) `E_k = -2E_p`

d) `E_k = 2E_p`

Using Bohr’s postulates, obtain the expression for total energy of the electron in the n^{th} orbit of hydrogen atom.

The electron in hydrogen atom is initially in the third excited state. What is the maximum number of spectral lines which can be emitted when it finally moves to the ground state?

Using Bohr’s postulates for hydrogen atom, show that the total energy (E) of the electron in the stationary states tan be expressed as the sum of kinetic energy (K) and potential energy (U), where K = −2U. Hence deduce the expression for the total energy in the n^{th} energy level of hydrogen atom.

Balmer series was observed and analysed before the other series. Can you suggest a reason for such an order?

Suppose, the electron in a hydrogen atom makes transition from *n* = 3 to *n* = 2 in 10^{−8} s. The order of the torque acting on the electron in this period, using the relation between torque and angular momentum as discussed in the chapter on rotational mechanics is

When a photon stimulates the emission of another photon, the two photons have

(a) same energy

(b) same direction

(c) same phase

(d) same wavelength

Evaluate Rydberg constant by putting the values of the fundamental constants in its expression.

According to Maxwell's theory of electrodynamics, an electron going in a circle should emit radiation of frequency equal to its frequency of revolution. What should be the wavelength of the radiation emitted by a hydrogen atom in ground state if this rule is followed?

A beam of light having wavelengths distributed uniformly between 450 nm to 550 nm passes through a sample of hydrogen gas. Which wavelength will have the least intensity in the transmitted beam?

A parallel beam of light of wavelength 100 nm passes through a sample of atomic hydrogen gas in ground state. (a) Assume that when a photon supplies some of its energy to a hydrogen atom, the rest of the energy appears as another photon. Neglecting the light emitted by the excited hydrogen atoms in the direction of the incident beam, what wavelengths may be observed in the transmitted beam? (b) A radiation detector is placed near the gas to detect radiation coming perpendicular to the incident beam. Find the wavelengths of radiation that may be detected by the detector.

A neutron having kinetic energy 12.5 eV collides with a hydrogen atom at rest. Nelgect the difference in mass between the neutron and the hydrogen atom and assume that the neutron does not leave its line of motion. Find the possible kinetic energies of the neutron after the event.

When a photon is emitted by a hydrogen atom, the photon carries a momentum with it. (a) Calculate the momentum carries by the photon when a hydrogen atom emits light of wavelength 656.3 nm. (b) With what speed does the atom recoil during this transition? Take the mass of the hydrogen atom = 1.67 × 10^{−27} kg. (c) Find the kinetic energy of recoil of the atom.

Suppose in an imaginary world the angular momentum is quantized to be even integral multiples of *h*/2π. What is the longest possible wavelength emitted by hydrogen atoms in visible range in such a world according to Bohr's model?

State any two Bohr’s postulates and write the energy value of the ground state of the hydrogen atom.

If l_{3} and l_{2} represent angular momenta of an orbiting electron in III and II Bohr orbits respectively, then l_{3}: l_{2} is :

Calculate angular momentum of an electron in the third Bohr orbit of a hydrogen atom.

Draw energy level diagram for a hydrogen atom, showing the first four energy levels corresponding to n=1, 2, 3 and 4. Show transitions responsible for:**(i)** Absorption spectrum of Lyman series.**(ii)** The emission spectrum of the Balmer series.

How are various lines of Lyman series formed? Explain on the basis of Bohr’s theory.

Write postulates of Bohr’s Theory of hydrogen atom.

Mention demerits of Bohr’s Atomic model.

The dissociation constant of a weak base (BOH) is 1.8 × 10^{−5}. Its degree of dissociation in 0.001 M solution is ____________.

According to Bohr's theory, an electron can move only in those orbits for which its angular momentum is integral multiple of ____________.

What is the energy in joules released when an electron moves from n = 2 to n = 1 level in a hydrogen atom?

The spectral line obtained when an electron jumps from n = 5 to n = 2 level in hydrogen atom belongs to the ____________ series.

A particle has a mass of 0.002 kg and uncertainty in its velocity is 9.2 × 10^{−6} m/s, then uncertainty in position is ≥ ____________.

(h = 6.6 × 10^{−34} J s)

The energy associated with the first orbit of He^{+} is ____________ J.

**Which of the following is/are CORRECT according to Bohr's atomic theory?**

(I) Energy is emitted when electron moves from a higher stationary state to a lower one.

(II) Orbits are arranged concentrically around the nucleus in an increasing order of energy.

(III) The energy of an electron in the orbit changes with time.

According to Bohr’s theory, the angular momentum of an electron in 5th orbit is ______.

For an electron in the second orbit of hydrogen, what is the moment of momentum as per the Bohr's model?

In Bohr model of hydrogen atom, which of the following is quantised?

According to Bohr's model of hydrogen atom, an electron can revolve round a proton indefinitely, if its path is ______.

If the radius of first electron orbit in hydrogen atom be r then the radius of the fourth orbit ill be ______.

The energy of an electron in an excited hydrogen atom is - 3.4 eV. Calculate the angular momentum of the electron according to Bohr's theory. (h = 6.626 × 10^{-34} Js)

Hydrogen atom has only one electron, so mutual repulsion between electrons is absent. However, in multielectron atoms mutual repulsion between the electrons is significant. How does this affect the energy of an electron in the orbitals of the same principal quantum number in multielectron atoms?

On the basis of Bohr's model, the approximate radius of Li^{++} ion in its ground state ifthe Bohr radius is a_{0} = 53 pm :

According to the Bohr theory of H-atom, the speed of the electron, its energy and the radius of its orbit varies with the principal quantum number n, respectively, as:

In form of Rydberg's constant R, the wave no of this first Ballmer line is

The wavelength of the first time line of Ballmer series is 6563 A°. The Rydberg constant for hydrogen is about:-

The angular momentum of electron in n^{th} orbit is given by

The energy of an electron in h^{th} orbit of hydrogen atom is –13.6/n^{2}ev energy required to excite the electron from the first orbit to the third orbit is

According to Bhor' s theory the moment of momentum of an electron revolving in second orbit of hydrogen atom will be.

The ratio of the ionization energy of H and Be^{+3} is ______.

The simple Bohr model cannot be directly applied to calculate the energy levels of an atom with many electrons. This is because ______.

Using Bohr model, calculate the electric current created by the electron when the H-atom is in the ground state.

If a proton had a radius R and the charge was uniformly distributed, calculate using Bohr theory, the ground state energy of a H-atom when (i) R = 0.1 Å, and (ii) R = 10 Å.

The inverse square law in electrostatics is |F| = `e^2/((4πε_0).r^2)` for the force between an electron and a proton. The `(1/r)` dependence of |F| can be understood in quantum theory as being due to the fact that the ‘particle’ of light (photon) is massless. If photons had a mass m_{p}, force would be modified to |F| = `e^2/((4πε_0)r^2) [1/r^2 + λ/r]`, exp (– λr) where λ = m_{p}c/h and h = `h/(2π)`. Estimate the change in the ground state energy of a H-atom if m_{p} were 10^{-6} times the mass of an electron.

Given below are two statements:

**Statements I:** According to Bohr's model of an atom, qualitatively the magnitude of velocity of electron increases with decrease in positive charges on the nucleus as there is no strong hold on the electron by the nucleus.

**Statement II: **According to Bohr's model of an atom, qualitatively the magnitude of velocity of electron increase with a decrease in principal quantum number.

In light of the above statements, choose the most appropriate answer from the options given below:

The value of angular momentum for He^{+} ion in the first Bohr orbit is ______.

The wavelength in Å of the photon that is emitted when an electron in Bohr orbit with n = 2 returns to orbit with n = 1 in H atom is ______ Å. The ionisation potential of the ground state of the H-atom is 2.17 × 10^{−11} erg.

The number of times larger the spacing between the energy levels with n = 3 and n = 8 spacing between the energy level with n = 8 and n = 9 for the hydrogen atom is ______.

An electron in H-atom makes a transition from n = 3 to n = 1. The recoil momentum of the H-atom will be ______.

Find the ratio of energies of photons produced due to transition of an election of hydrogen atom from its (i) second permitted energy level to the first level. and (ii) the highest permitted energy level to the first permitted level.

A hydrogen atom in its first excited state absorbs a photon of energy x × 10^{-2} eV and exited to a higher energy state where the potential energy of electron is -1.08 eV. The value of x is ______.

In Bohr's atomic model of hydrogen, let K. P and E are the kinetic energy, potential energy and total energy of the electron respectively. Choose the correct option when the electron undergoes transitions to a higher level:

The electron in a hydrogen atom first jumps from the third excited state to the second excited state and subsequently to the first excited state. The ratio of the respective wavelengths, λ_{1}/λ_{2}, of the photons emitted in this process is ______.

The energy required to remove the electron from a singly ionized Helium atom is 2.2 times the energy required to remove an electron from Helium atom. The total energy required to ionize the Helium atom completely is ______.

Orbits of a particle moving in a circle are such that the perimeter of the orbit equals an integer number of de-Broglie wavelengths of the particle. For a charged particle moving in a plane perpendicular to a magnetic field, the radius of the n^{th} orbital will therefore be proportional to:

If 13.6 eV energy is required to ionize the hydrogen atom, then the energy required to remove an electron from n = 2 is ______.

The first ionization energy of H is 21.79 × 10^{-19} J. The second ionization energy of He atom is ______ × 10^{-19}J.

The line at 434 nm in the Balmer series of the hydrogen spectrum corresponds to a transition of an electron from the n^{th }to second Bohr orbit. The value of n is ______.

A 100 eV electron collides with a stationary helium ion (He^{+}) in its ground state and exits to a higher level. After the collision, He^{+} ions emit two photons in succession with wavelengths 1085 Å and 304 Å. The energy of the electron after the collision will be ______ eV.

Given h = 6.63 × 10^{-34} Js.

The energy of an electron in the first Bohr orbit of the H-atom is −13.6 eV. The energy value of an electron in the excited state of Li^{2+} is ______.

A hydrogen atom in is ground state absorbs 10.2 eV of energy. The angular momentum of electron of the hydrogen atom will increase by the value of ______.

(Given, Planck's constant = 6.6 × 10^{-34} Js)

What is the energy associated with first orbit of Li^{2+} (R_{H} = 2.18 × 10^{-18})?

In hydrogen atom, transition from the state n = 6 to n = 1 results in ultraviolet radiation. Infrared radiation will be obtained in the transition ______.

In Bohr's theory of hydrogen atom, the electron jumps from higher orbit n to lower orbit p. The wavelength will be minimum for the transition ______.

A 20% efficient bulb emits light of wavelength 4000 Å. If the power of the bulb is 1 W, the number of photons emitted per second is ______.

[Take, h = 6.6 × 10^{-34} J-s]

What is the energy of an electron in stationary state corresponding to n = 2?

According to Bohr's theory, the radius of the nth Bohr orbit of a hydrogen like atom of atomic number Z is proportional to ______.

Oxygen is 16 times heavier than hydrogen. Equal volumes of hydrogen and oxygen are mixed. The ratio of speed of sound in the mixture to that in hydrogen is ______.

The total energy of an electron in the nth orbit of the hydrogen atom is proportional to ______.

Hydrogen atom from excited state comes to the ground state by emitting a photon of wavelength λ. If R is the Rydberg constant then the principal quantum number n of the excited state is ______.

An electron in a hydrogen atom has an energy of -3.4 eV. The difference between its kinetic and potential energy is ______.

How much is the angular momentum of an electron when it is orbiting in the second Bohr orbit of hydrogen atom?