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Q13Q

Expert-verifiedFound in: Page 1181

Book edition
10th Edition

Author(s)
David Halliday

Pages
1328 pages

ISBN
9781118230718

**The following nonrelativistic particles all have the same kinetic energy. Rank them in order of their de Broglie wavelengths, greatest first: electron, alpha particle, neutron.**

** **

The rank is electron, neutron, alpha particle.

**The de Broglie wavelength is given by, **

**${\mathit{\lambda}}{\mathbf{=}}\frac{\mathbf{h}}{\mathbf{m}\mathbf{v}}$**

**Here, h is the plank’s constant, m is the mass and v is the velocity.**

From the de Broglie wavelength, it can be observed that the mass of the particle is inversely proportional to the wavelength.

It is known that the mass of the neutron is ${m}_{n}=1.67\times {10}^{-27}\text{kg}$ , the mass of alpha particle is ${m}_{\alpha}=6.664\times {10}^{-27}\text{kg}$ and the mass of the electron is ${m}_{e}=9.11\times {10}^{-31}\text{kg}$. Clearly, ${m}_{e}<{m}_{n}<{m}_{\alpha}$ . So, rank of de Broglie wavelength is ${\lambda}_{\text{e}}>{\lambda}_{n}>{\lambda}_{\alpha}$ .

Therefore, the rank is electron, neutron, alpha particle.

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