An electron beam is accelerated by a potential difference V to hit a metallic target to produce X-rays. It produces continuous as well as characteristic X-rays. If $\lambda_{\text {min }}$ is the smallest possible wavelength of X-ray in the spectrum, the variation of $\log \lambda_{\text {min }}$ with $\log \mathrm{V}$ is correctly represented in :

JEE Main · 2017 · 02 Apr 2017 · Offline · Modern Physics

An electron beam is accelerated by a potential difference V to hit a metallic target to produce X-rays. It produces continuous as well as characteristic X-rays. If

λ_{min}

is the smallest possible wavelength of X-ray in the spectrum, the variation of

lo g λ_{min}

with

lo g V

is correctly represented in :

(A)(see structure)
(B)(see structure)
✓ Correct
(C)(see structure)
(D)(see structure)

Answer: (B)

Solution

The shortest wavelength comes from the full accelerating energy landing in one photon:

e V = \frac{h c}{λ _{m i n}}

, so

λ_{m i n} = \frac{h c}{e V}

. Taking logarithms,

lo g λ_{m i n} = lo g \frac{h c}{e} - lo g V

— a straight line against

lo g V

with slope

- 1

and a positive intercept. The graph that falls steadily with unit negative slope is the correct one.

JEE Main · 2017 · 02 Apr 2017 · Offline · Single correct option

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