What is the energy of a photon that has a wavelength equal to the de Broglie wavelength of a proton having a speed of 7.1 × m/s? (m_proton = 1.67 × 10^-27 kg,c = 3.00 × 10⁸ m/s) A)220 keV B)150 keV C)290 keV D)360 keV E)440 keV

Question

Quizplus · Accepted Answer

We can use the de Broglie wavelength formula to find the wavelength of the proton:
λ = h/p
where h is Planck's constant and p is the momentum of the proton.
p = mv = (1.67 × 10^-27 kg)(7.1 × 10^5 m/s) = 1.185 × 10^-19 kg*m/s
λ = (6.626 × 10^-34 J*s)/(1.185 × 10^-19 kg*m/s) = 5.59 × 10^-15 m
Now, we can use the formula for the energy of a photon:
E = hc/λ
where c is the speed of light.
E = (6.626 × 10^-34 J*s)(3.00 × 10^8 m/s)/(5.59 × 10^-15 m) = 3.56 × 10^-11 J
Convert to keV:
E = 3.56 × 10^-11 J / (1.602 × 10^-16 J/keV) = 222 keV
The closest answer choice is A, 220 keV.

What Is the Energy of a Photon That Has a Wavelength