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de Broglie proposed dual nature for elec...

de Broglie proposed dual nature for electron by putting his famous equation `lambda = (h)/(mv).` Later on, Heisenberg proposed uncertainty principle as `deltapDeltax ge (h)/(4pi).` On the contrary,
Particle nature of electron was established on the basis of photoelectric effect. When a photon strikes the metal surface it gives up its energy to the electron. Part of this energy (say W) is used by the electrons to escape from the metal and the remaining energy imparts kinetic energy `(1//2 mv^(2))` to the ejected photoelectron. The potential applied on the surface to reduce the velocity of photoelectron to zero is known as stopping potential .
When a beam of photons of a particular energy was incident on a surface of a particular pure metal having work function =(40 eV), some emitted photoelectrons had stopping potential equal to 22 V. some had 12V and rest had lower values. Calculate the wavelength of incident photons assuming that at least one photoelectron is ejected with maximum possible kinetic energy :

A

`310 Å`

B

`298 Å`

C

`238 Å`

D

`200 Å`

Text Solution

Verified by Experts

The correct Answer is:
D
The maximum `KE` of potoelectron is corresponding to maximum stopping `=22 eV`
`:. E_("incident")=E_("threshold")+KE_(maxi)=40 eV+22 eV=62 eV`
`lambda_("incident")=(12400 Å)/(62)=200 Å`
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