Monochromatic radiation emitted when electron on hydrogen atom jumps from first excited to the ground state irradiates on a photosensitive material. The stopping potential is measured to be 3.57V. The threshold frequency of the material is :
A
1.6×1015Hz
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B
2.5×1015Hz
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C
4×1015Hz
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D
5×1015Hz
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Solution
The correct option is A1.6×1015Hz For hydrogen atom the energy in nth state is En=−13.6eVn2
First excited state means second normal state i.e. n=2
ground state is n=1 so the energy of emitted photon will be E=−(E1−E2)=−13.6eV(−1+14)=10.2eV
Stopping potential V0=3.57volt
on using Einstein equation, eV0=E−W, W is work function
so W=(10.2−3.57)eV=6.63eV=6.63×1.6×10−19joule=1.0608×10−18Joule
the threshold frequency , f0=Wh ......(1)
h is Planck's constant h=6.62×10−34Js
putting these values in equation-1 , we get f0=1.6×1015Hz