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Q12Q

Expert-verifiedFound in: Page 1181

Book edition
10th Edition

Author(s)
David Halliday

Pages
1328 pages

ISBN
9781118230718

**An electron and a proton have the same kinetic energy. Which has the greater de Broglie wavelength?**

The electron has greater de Broglie wavelength than proton.

**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 proton is ${m}_{p}=1.67\times {10}^{-27}\text{kg}$ and the mass of the electron is ${m}_{e}=9.11\times {10}^{-31}\text{kg}$. Clearly, the mass of the proton is more than the mass of the electron. So, the de Broglie wavelength of electron will be more than the de Broglie wavelength of proton.

Therefore, the electron has greater de Broglie wavelength than proton.

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