A ball moving with a speed of \(12\ \mathrm{m\,s^{-1}}\) has a de Broglie wavelength of \(1.0\times10^{-33}\ \mathrm{m}\). The mass of the ball is (Take \(h = 6.6\times10^{-34}\ \mathrm{J\,s}\).)
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → 0.055 kg
The de Broglie relation \( \lambda=h/mv \) connects the wavelength of a moving body with its mass and speed. So the mass is \( m=h/\lambda v \).
\( \begin{aligned} m &= \frac{h}{\lambda v} \\ &= \frac{6.6\times10^{-34}}{1.0\times10^{-33}\times12} \\ &= 0.055\ \mathrm{kg} \end{aligned} \)
Therefore, the mass of the ball is 0.055 kg.
NCERT (2026-27):
Wave Nature of Matter – “… De Broglie proposed that the wave length λ associated with a particle of momentum p is given as”
\( \displaystyle \lambda=\frac{h}{p}=\frac{h}{mv} \)\( \qquad (11.5) \)
“where m is the mass of the particle and v its speed.”