Can't get my head around reduced mass (particle physics)

[Flucky]

I know it's probably simple but I just don't understand reduced mass.

I am trying to work out the reduced mass of ⁴He⁺.

m = m_em_N / m_e + m_N

Can somebody please just explain step by step what I do. This is only a segment of a 1 mark question and I'm getting my knickers in a frustratingly twisty twist. I've looked at the other threads and websites but still no clue.

The answer needs to be 3.99... but I always end up with 0.99...

 

[Orodruin]

Normally you would need to expand more than that on your attempted solution, but I have a suspicion.

What are the units you are quoting your answers in? Atomic mass units? In that case, did you insert the mass of one nucleon instead of that of a helium nucleus?

 

[Flucky]

Hi Orodruin

I'll give you the full question to give a better understanding-

Calculate the wavelength of the n = 4 → 3 transition in ⁴He⁺ to an accuracy of 4 significant figures. (R∞=109 737 cm^-1.) (Fine structure effects can be neglected.)

Now the equation that I'd use for this is:

$\frac{1}{λ} = \frac{m}{m_e} R_∞ (\frac{1}{n_1^2} - \frac{1}{n_2^2})$

Where λ is wavelength, m is the reduced mass, and $R_∞$ is Rydberg constant.

So I know the answer for the wavelength is 468.7 nm (I looked), and working backwards to try make sense of reduced mass I got m = 3.99.

I tried it in SI units using the mass in kg of an electron + 2 protons + 2 neutrons but it still didn't help.

 

[Flucky]

I will create a new thread with proper formatting, and pose the question as a whole - so could you delete this thread please?

Edit: properly formatted thread at https://www.physicsforums.com/threads/calculate-the-wavelength-of-the-n-4-3-transition-in-he.791525/