Electromagnetic Question

[niel23]

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If an ion with velocity v, mass m, and charge z enters a magnetic field and emits a photon of red light, what would the same particle with velocity 1/2 v emit?

a. x - ray
b. Ultra-violet
c. Blue light
d. Infrared light


The answer explanation says that a particle with lower velocity will emit light with lower frequency and therefore the answer is D. I'm having trouble wrapping my head around this since I thought,

given v = lambda x frequency

And since we're not in a vacuum, therefore, light will travel at different speeds. Lower speed is associated with higher frequency, the opposite of what the answer is. Red light (700 nm /2) = 350 nm --> ultraviolet light.

:/

Some insight will be great. Thank you!

 

[aldol16]

I'll explain it de novo. The same particle with half the velocity would have a quarter of the kinetic energy by a simple E = 0.5*m*v^2 argument. Or, even more broadly, it will have less kinetic energy than the original simply because it's traveling slower. That allows you to rule out all but D right there because lower energy means shift to longer wavelengths. But let's see this through. If you have a quarter of the energy, you must also have 4 times the wavelength by the equation E = hc/lambda. Thus, the wavelength would be longer and the only answer choice with wavelength longer than visible light is D.

 

[niel23]

That explanation was very helpful.

Thank you!