Advertisements
Advertisements
Question
A beam of monochromatic light of wavelength λ ejects photoelectrons from a cesium surface (Φ = 1.9 eV). These photoelectrons are made to collide with hydrogen atoms in ground state. Find the maximum value of λ for which (a) hydrogen atoms may be ionized, (b) hydrogen atoms may get excited from the ground state to the first excited state and (c) the excited hydrogen atoms may emit visible light.
Advertisements
Solution
Given:
Work function of cesium surface, ϕ = 1.9 eV
(a) Energy required to ionise a hydrogen atom in its ground state, E = 13.6 eV
From the Einstein's photoelectric equation,
`(hc)/lamda = E + Ø`
Here,
h = Planck's constant
c = Speed of light
λ = Wavelength of light
`therefore (hc)/lamda = 1.9 = 13.6`
`rArr 1240/lamda = 15.5`
`rArr lamda =(1240)/15.5 `
`rArr lamda = 80 nm`
(b) When the electron is excited from the states n1 = 1 to n2 = 2, energy absorbed (E1) is given by
`E_1 = 13.6 (1/n_1^2 - 1/n_2^2)`
`E_1 = 13.6 (1- 1/4)`
`E_1 = (13.66xx3)/4`
For Einstein's photoelectric equation,
`therefore (hc)/lamda - 1.9 = (13.6xx3)/4`
`rArr (hc)/lamda = (13.6xx3)/4 + 1.9`
`1240/(lamda) = 10.2 + 1.9 =12.1`
`rArr lamda = (1240)/12.1`
`lamda = 102.47 = 102 nm `
(c) Excited atom will emit visible light if an electron jumps from the second orbit to third orbit, i.e. from n1 = 2 to n2 = 3. This is because Balmer series lies in the visible region.
Energy (E2) of this transition is given by
`E_2 = 13.6 (1/n_1^2 - 1/n_2^2)`
`E_2 = 13.6 (1/4 - 1/9)`
`E_2 = (13.66xx5)/(36)`
For Einstein's photoelectric equation,
`(hc)/lamda - 1.9 = (13.6xx5)/36`
`rArr (hc)/lamda = (13.6xx5)/36+ 1.9 `
`rArr 1240/lamda = 1.88 + 1..9 = 3.78`
`rArr lamda = 1240/3.78`
`rArr lamda = 328.04 nm
APPEARS IN
RELATED QUESTIONS
How many electrons in an atom may have the following quantum numbers?
n = 4, `m_s = -1/2`
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`
On the basis of Bohr's theory, derive an expression for the radius of the nth orbit of an electron of the hydrogen atom.
Using Bohr's postulates, derive the expression for the total energy of the electron in the stationary states of the hydrogen atom ?
The numerical value of ionization energy in eV equals the ionization potential in volts. Does the equality hold if these quantities are measured in some other units?
The Bohr radius is given by `a_0 = (∈_0h^2)/{pime^2}`. Verify that the RHS has dimensions of length.
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.
When the electron orbiting in hydrogen atom in its ground state moves to the third excited state, show how the de Broglie wavelength associated with it would be affected.
Write postulates of Bohr’s Theory of hydrogen atom.
For an electron in the second orbit of hydrogen, what is the moment of momentum as per the Bohr's model?
Which of these statements correctly describe the atomic model according to classical electromagnetic theory?
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:
The binding energy of a H-atom, considering an electron moving around a fixed nuclei (proton), is B = `- (Me^4)/(8n^2ε_0^2h^2)`. (m = electron mass). If one decides to work in a frame of reference where the electron is at rest, the proton would be moving around it. By similar arguments, the binding energy would be
B = `- (Me^4)/(8n^2ε_0^2h^2)` (M = proton mass)
This last expression is not correct because ______.
Use Bohr's postulate to prove that the radius of nth orbit in a hydrogen atom is proportional to n2.
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:
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 ______.
What is meant by ionisation energy?
Specify the transition of an electron in the wavelength of the line in the Bohr model of the hydrogen atom which gives rise to the spectral line of the highest wavelength ______.
The energy of an electron in the nth orbit of the hydrogen atom is En = -13.6/n2eV. The negative sign of energy indicates that ______.
