Question

The electron beam in a colour TV is accelerated through $32\text{kV}$ and then strikes the screen. What is the wavelength of the most energetic X-ray photon? $(hc=1242\text{eV-nm})$

• A. $38.8\text{pm}$
• B. $48.8\text{pm}$
• C. $58.8\text{pm}$
• D. $68.8\text{pm}$

Answer 1

The correct option is A $38.8\text{pm}$

Given, $V=32\text{kV}=32\times {10}^3\text{V}$

When electron beam is accelerated through $32\text{kV}$, the energy supplied be

$E=32\times {10}^3\text{eV}$,

$\Rightarrow \lambda =\frac{hc}{E}=\frac{1242\text{eV-nm}}{32\times {10}^3\text{eV}}$

$=38.8\times {10}^{-3}\text{nm}=38.8\text{pm}$

Hence, $\left(A\right)$ is the correct answer.

Why this question? Caution: Be careful with the unit while substituting the values of $hc$ and $\lambda$.