Q157 / 160 · TS EAMCET 2015 · Physics
If an electron has an energy such that its de-Broglie wavelength is $5500 Å$, then the energy value of that electron is $\left(h=6.6 \times 10^{-34} \mathrm{Js}, m_{\mathrm{c}}=9.1 \times 10^{-31} \mathrm{~kg}\right)$
- A$8 \times 10^{-20} \mathrm{~J}$
- B$8 \times 10^{-10} \mathrm{~J}$
- C$8 \mathrm{~J}$
- Correct answerD$8 \times 10^{-25} \mathrm{~J}$
Solution
de-Broglie wavelength
$$
\begin{aligned}
\lambda & =\frac{h}{\sqrt{2 m E}} \\
E & =\frac{1}{2 m}\left(\frac{h}{\lambda}\right)^2
\end{aligned}
$$
$$
\begin{aligned}
& =\frac{1}{2 \times 9.1 \times 10^{-31}}\left(\frac{6.625 \times 10^{-34}}{5.5 \times 10^{-7}}\right)^2 \\
& =\frac{1}{18.2 \times 10^{-31}} \times 1.45 \times 10^{-54} \\
& =8 \times 10^{-25} \mathrm{~J}
\end{aligned}
$$
Hence, the correct answer is option: 'D'.