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Photon and electron are given same energ...

Photon and electron are given same energy `(10^(-20) J)`. Wavelength associated with photon and electron are `lambda_(ph)` and `lambda_(el)` then correct statement will be

A

`lamda_(ph) = lamda_(e)`

B

`lamda_(ph) lt lamda_(e)`

C

`lamda_(e)//lamda_(ph) = c`

D

`lamda_(ph) gt lamda_(e)`

Text Solution

Verified by Experts

The correct Answer is:
D
`E_(ph) = E_(e)`
`rArr (hc)/(lamda_(ph))= ((h//lamda_(e))^(2))/(2m_(e))` momentum of electron `= (lamda)/(lamda_(e))`
`rArr (c )/(lamda_(ph))= (h)/(2lamda_(e)^(2) m_(e))`
`rArr (lamda_(ph))/(lamda_(e))= (2c lamda_(e) m e)/(h)`
`lamda_(e) = (h)/(sqrt(2m_(e)E_(2)))`
`therefore (lamda_(ph))/(lamda_(e)) =c sqrt((2m_(e))/(E_(e)))=c sqrt((2 xx 9.1 xx 10^(-31))/(10^(-20)))`
`=1.35 xx 10^(-5) xx 3 xx 10^(8) = 4 xx 10^(3)`
`lamda_(ph) gt lamda_(e)`
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