JEE Main · 2021 · 24 Feb 2021 · Shift 2 · Modern Physics

An X - ray tube is operated at 1.24 million volt. The shortest wavelength of the produced photon will be:

(A) $1 0^{- 4} nm$
(B) $1 0^{- 3} nm$ ✓ Correct
(C) $1 0^{- 1} nm$
(D) $1 0^{- 2} nm$

Answer: (B)

Solution

The shortest wavelength is emitted when an electron gives up its entire kinetic energy

e V

to a single photon, so

\frac{h c}{λ _{m i n}} = e V

and

λ_{m i n} = \frac{h c}{e V} = \frac{( 6.63 \times 1 0 ^{- 34} ) ( 3 \times 1 0 ^{8} )}{( 1.6 \times 1 0 ^{- 19} ) ( 1.24 \times 1 0 ^{6} )} = 1 \times 1 0^{- 12} m

Since

1 nm = 1 0^{- 9}

m, the shortest wavelength of the photon produced is

1 0^{- 3}

nm.

JEE Main · 2021 · 24 Feb 2021 · Shift 2 · Single correct option

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