Atomic StructureHard
Question
A electron in the hydrogen atom jumped from excited state n to the ground state. The wavelength so emitted illuminates a photosensitive material having work function 2.75 eV. If the stopping potential of the photoelectron is 10 V, then the value of n is
Options
A.2
B.3
C.4
D.5
Solution
Here, stopping potential, V0 = 10V
Work function, W = 2.75 eV
According to Einstein′s photoelectric equation
or
= 10 eV + 2.75 eV = 12.75 eV ...... (i)
When an electron in the hydrogen atom makes a transition from excited state n to the ground state (n = 1), then he frequency (
) of the emitted photon is given by
h = En - E1
h = - 
[∵ For hydrogen atom, En =
]
According to the given problem
+ 13.6 = 12.75 [Using (i)]
= 0.85 ⇒ n2 = 
or n = 4
Work function, W = 2.75 eV
According to Einstein′s photoelectric equation
or
= 10 eV + 2.75 eV = 12.75 eV ...... (i)
When an electron in the hydrogen atom makes a transition from excited state n to the ground state (n = 1), then he frequency (
) of the emitted photon is given by h
= En - E1h
= - [∵ For hydrogen atom, En =
]According to the given problem
+ 13.6 = 12.75 [Using (i)] = 0.85 ⇒ n2 = or n = 4
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