Advertisements
Advertisements
प्रश्न
A 12.5 eV electron beam is used to bombard gaseous hydrogen at room temperature. What series of wavelengths will be emitted?
Advertisements
उत्तर
It is given that the energy of the electron beam used to bombard gaseous hydrogen at room temperature is 12.5 eV. Also, the energy of the gaseous hydrogen in its ground state at room temperature is −13.6 eV.
When gaseous hydrogen is bombarded with an electron beam, the energy of the gaseous hydrogen becomes −13.6 + 12.5 eV i.e., −1.1 eV.
Orbital energy is related to orbit level (n) as:
E = `(-13.6)/(n)^2 ev`
For n = 3, E = `(-13.6)/9` = −1.5 eV
This energy is approximately equal to the energy of gaseous hydrogen. It can be concluded that the electron has jumped from n = 1 to n = 3 level.
During its de-excitation, the electrons can jump from n = 3 to n = 1 directly, which forms a line of the Lyman series of the hydrogen spectrum.
We have the relation for wave number for the Lyman series as:
`1/lambda = R_y (1/1^2 - 1/n^2)`
Where
Ry = Rydberg constant = 1.097 × 107 m−1
λ = Wavelength of radiation emitted by the transition of the electron
For n = 3, we can obtain λ as:
`1/lambda = 1.0997 xx 10^7 (1/1^2 - 1/3^2)`
= `1.097 xx 10^7 (1 - 1/9)`
= `1.097 xx 10^7 xx 8/9`
`lambda = 9/(8 xx 1.097 xx 10^7)`
= 102.55 nm
If the electron jumps from n = 2 to n = 1, then the wavelength of the radiation is given as:
`1/lambda = 1.097 xx 10^7 (1/1^2 - 1/2^2)`
= `1.097 xx 10^7(1- 1/4)`
= `1.097 xx 10^7 xx 3/4`
`lambda = 4/(1.097 xx 10^7 xx 3)`
= 121.54 nm
If the transition takes place from n = 3 to n = 2, then the wavelength of the radiation is given as:
`1/lambda = 1.097 xx 10^7 (1/2^2 - 1/3^2)`
`= 1.097 xx 10^7 (1/4 - 1/9)`
= `1.097 xx 10^7 xx 5/36`
= `36 /(5xx1.097 xx 10^7)`
= 656.33 nm
This radiation corresponds to the Balmer series of the hydrogen spectrum.
Hence, in the Lyman series, two wavelengths, i.e., 102.55 nm and 121.54 nm, are emitted. And in the Balmer series, one wavelength, i.e., 656.33 nm, is emitted.
संबंधित प्रश्न
When white radiation is passed through a sample of hydrogen gas at room temperature, absorption lines are observed in Lyman series only. Explain.
In which of the following transitions will the wavelength be minimum?
Which of the following curves may represent the speed of the electron in a hydrogen atom as a function of trincipal quantum number n?
A hydrogen atom in ground state absorbs 10.2 eV of energy. The orbital angular momentum of the electron is increased by
An electron with kinetic energy 5 eV is incident on a hydrogen atom in its ground state. The collision
Let An be the area enclosed by the nth orbit in a hydrogen atom. The graph of ln (An/A1) against ln(n)
(a) will pass through the origin
(b) will be a straight line with slope 4
(c) will be a monotonically increasing nonlinear curve
(d) will be a circle
Find the binding energy of a hydrogen atom in the state n = 2.
(a) Find the first excitation potential of He+ ion. (b) Find the ionization potential of Li++ion.
A hydrogen atom in state n = 6 makes two successive transitions and reaches the ground state. In the first transition a photon of 1.13 eV is emitted. (a) Find the energy of the photon emitted in the second transition (b) What is the value of n in the intermediate state?
Find the maximum angular speed of the electron of a hydrogen atom in a stationary orbit.
The average kinetic energy of molecules in a gas at temperature T is 1.5 kT. Find the temperature at which the average kinetic energy of the molecules of hydrogen equals the binding energy of its atoms. Will hydrogen remain in molecular from at this temperature? Take k = 8.62 × 10−5 eV K−1.
Find the temperature at which the average thermal kinetic energy is equal to the energy needed to take a hydrogen atom from its ground state to n = 3 state. Hydrogen can now emit red light of wavelength 653.1 nm. Because of Maxwellian distribution of speeds, a hydrogen sample emits red light at temperatures much lower than that obtained from this problem. Assume that hydrogen molecules dissociate into atoms.
Average lifetime of a hydrogen atom excited to n = 2 state is 10−8 s. Find the number of revolutions made by the electron on the average before it jumps to the ground state.
Show that the ratio of the magnetic dipole moment to the angular momentum (l = mvr) is a universal constant for hydrogen-like atoms and ions. Find its value.
The Balmer series for the H-atom can be observed ______.
- if we measure the frequencies of light emitted when an excited atom falls to the ground state.
- if we measure the frequencies of light emitted due to transitions between excited states and the first excited state.
- in any transition in a H-atom.
- as a sequence of frequencies with the higher frequencies getting closely packed.
Let En = `(-1)/(8ε_0^2) (me^4)/(n^2h^2)` be the energy of the nth level of H-atom. If all the H-atoms are in the ground state and radiation of frequency (E2 - E1)/h falls on it ______.
- it will not be absorbed at all.
- some of atoms will move to the first excited state.
- all atoms will be excited to the n = 2 state.
- no atoms will make a transition to the n = 3 state.
Positronium is just like a H-atom with the proton replaced by the positively charged anti-particle of the electron (called the positron which is as massive as the electron). What would be the ground state energy of positronium?
In the Auger process an atom makes a transition to a lower state without emitting a photon. The excess energy is transferred to an outer electron which may be ejected by the atom. (This is called an Auger electron). Assuming the nucleus to be massive, calculate the kinetic energy of an n = 4 Auger electron emitted by Chromium by absorbing the energy from a n = 2 to n = 1 transition.
A hydrogen atom makes a transition from n = 5 to n = 1 orbit. The wavelength of photon emitted is λ. The wavelength of photon emitted when it makes a transition from n = 5 to n = 2 orbit is ______.
