Discussion
A muon from cosmic rays is trapped by a proton to form a hydrogen-like atom. Given that a muon is approximately 200 times heavier than an electron, the longest wavelength of the spectral line (in analogy with the Lyman series) of such an atom will be :
Answer: B
The wavelength is about 6.67 Å.
Energy levels of a hydrogen-like atom scale with the reduced mass. For a muon of about 200 electron masses bound to a proton (1836 electron masses), the reduced mass is about \(\frac{200 \times 1836}{2036} \approx 180\) electron masses, so every wavelength is about 180 times shorter than in hydrogen:
\[ \lambda \approx \frac{1216}{180} \approx 6.7 \]
in Ångström units, starting from hydrogen's Lyman-alpha line at 1216 Å.
The longest Lyman-type line is the 2 to 1 transition. The nearest option is 6.67 Å. Ignoring the reduced mass (dividing by 200) gives about 6.1 Å; 13.3, 5.62 and 3.75 Å are much further off.
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