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PhysicsModern PhysicsDe Broglie & Matter WavesMedium2 minQB

PhysicsMediumsingle choice

A photon, an electron and a uranium nucleus all have the same wavelength. The one with the most energy

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Answer:

Solution:

Same wavelength ⇒ same momentum $p = h / λ$ for all three. Photon: $E = p c$ . Electron (non-relativistic): $K = \frac{p ^{2}}{2 m _{e}}$ . Uranium nucleus: $K = \frac{p ^{2}}{2 M}$ , the smallest of all. $\frac{p ^{2}}{2 m _{e}} < p c$ whenever $p < 2 m_{e} c$ , i.e. $λ > \frac{h}{2 m _{e} c} \approx 1.2 pm$ , which covers every ordinary (optical/X-ray) wavelength. So $E_{photon} > K_{e} > K_{U}$ : the photon has the most energy.

Subject:PhysicsTopic:Modern PhysicsSubtopic:De Broglie & Matter Waves

⏱ 2mℹ️ Source: QB

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