QJEEAdv07Phb264: JEE Advanced 2007 Physics - Class 12 JEEAdv07Phb264 Solution: Electrons with de-Broglie wavelength λ fall on the target in an …

Question

Verified Solution • 2025–26 Session moderate

Electrons with de-Broglie wavelength $λ$ fall on the target in an X-ray tube. The cut-off wavelength of the emitted X-rays is

Accepted Answer

The cut off wavelength is given by

$λ_{0} = \frac{h c}{e v}$ ..... (i)

According to de-Broglie equation

$λ = \frac{h}{p} = \frac{h}{\sqrt{2 m e V}}$

$\Rightarrow λ^{2} = \frac{h^{2}}{2 m e V}$

$\Rightarrow V = \frac{h^{2}}{2 m e λ^{2}}$ ..... (ii)

From (i) and (ii)

$λ_{0} = \frac{h c \times 2 m e λ^{2}}{e h^{2}} = 2 m c λ^{2}$

Step-by-Step Verified Solution