The de-Broglie wavelength of photon is twice the de-Broglie wavelength of an electron .The speed of the electron is `v_(e)=(c )/(100)`.Then

Options

A. `(E_(e))/(E_(p))=10^(-4)`
B. `(E_(e))/(E_(p))=10^(-2)`
C. `(p_(e))/(m_(e)c)=10^(-2)`
D. `(p_(e))/(m_(e)c)=10^(-4)`

Answer

B, C

Explanation

For photon ,`E_(p)=(hc)/(lambda_(p))=(hc)/(2lambda_(e))`
(`because lambda_(p)=2lambda_(e)` is given)
For electron `E_(e)=(p_(e)^(2))/(2m_(e))=(1)/(2m_(e))((h^(2))/(lambda_(e)^(2)))`
`therefore (E_(e))/(E_(p))=(h^(2))/(2m_(2)lambda_(e)^(2))xx(2lambda_(e))/(hc)=(h)/(m_(e)c lambda_(e))`
`therefore (E_(e))/(E_(p))=(h)/(m_(e)c)xx(m_(e)v_(e))/(h)(because lambda_(e)=(h)/(m(e)v_(e)))`
`therefore (E_(e))/(E_(p))=(v_(e))/(c)=(1)/(100)(because v_(e)=(c)/(100)` is given)
`therefore`(E_(e))/(E_(p))=10^(-2)`
`implies` Option (B) is correct .
Now ,`(p_(e))/(m_(e)c)=(m_(e)v_(e))/(m_(e)c)=(v_(e))/(c)=10^(-2)`
`implies Option (C )is also correct.