What is the mass of a particle with a wavelength of \(3.313 Å\) moving with a speed of \(2.0 \times 10^8…
What is the mass of a particle with a wavelength of \(3.313 Å\) moving with a speed of \(2.0 \times 10^8 \mathrm{~ms}^{-1}\) ?
- \(1.0 \times 10^{-28} \mathrm{~kg}\)
- \(2.0 \times 10^{-32} \mathrm{~kg}\)
- \(1.0 \times 10^{-32} \mathrm{~kg}\)
- \(2.0 \times 10^{-28} \mathrm{~kg}\)
Solution
According to de-Broglie relation:
\(\lambda=\frac{h}{m v}\)
where,
\(h=\) Planck's constant \(=6.626 \times 10^{-34} \mathrm{Js}\)
\(v=\) speed of moving particle
\(m=\) mass of moving particle
\(\lambda=\) wavelength of particle.
Thus,
\(m=\frac{h}{\lambda \times v}\)
Given,
Speed (velocity) of moving particle \((v)=2 \times 10^8 \mathrm{~m} / \mathrm{s}\)
Wavelength of moving particle \((\lambda)=3.313 Å\)
\(=3313 \times 10^{-10} \mathrm{~m}\)
\(\begin{aligned}
\therefore \quad m & =\frac{6.626 \times 10^{-34}}{3.313 \times 2 \times 10^8 \times 10^{-10}} \\
m & =1 \times 10^{-32} \mathrm{~kg}
\end{aligned}\)
Hence, option (c) is correct.
Asked in: AP EAMCET 2019 (23 Apr Shift 1)
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