Question

If vacuum tube is operated at 6.4 kV, what is the wavelength of X-ray produced:-

• A. $1.93Ă$
• B. $1.53Ă$
• C. $2.67Ă$
• D. $0.78Ă$

Answer 1

The correct option is A

$1.93Ă$

Given

Operating voltage (V): $6.4kV=6.4\times {10}^{3}V$

Assume Planck's constant (h) = $6.67\times {10}^{-34}J/s$ ,

Speed of ray (c) = $3\times {10}^{8}m/s$

and electron charge (e) = $1.69\times {10}^{-19}C$

Finding wavelength

We know that,

$\lambda =\frac{hc}{eV}$, where $\lambda$ is wavelength.

$\Rightarrow \lambda =\frac{6.67\times {10}^{-34}\times 3\times {10}^8}{1.69\times {10}^{-19}\times 6.4\times {10}^3}$

$\Rightarrow \lambda =1.93\times {10}^{-10}m=1.93Ă$

Hence, the wavelength of X-ray produced is $1.93Ă$.

Hence, option A is correct.