Question

A hydrogen atom has an electron of mass m and a proton of mass M, M>>m. The reduced mass is defined to be:
u= mM/(m+M)
Given u as a series in m/M:
The 1st order correction term is defined by including the linear term by no higher order terms. If m = M/1836, by what percentage does including the 1st order correction change the estimate u=m?

Answer 1

did you do the series for mM / (m + M )

Answer 2

u= m * M / (m+M)
u = m* M * ( m + M ) ^ -1
u = m*M * [ M ( m/M + 1) ] ^ -1
u = m * M * M^-1 ( m/M + 1 )^-1
u = m * ( 1 + m/M) ^-1

Answer 3

now we can use the taylor series

( 1 + x) ^-1 = 1 - x + x^2 - x^3 + ...

Answer 4

u = m * ( 1 + m / M ) ^-1

u = m * [ 1 - m/M + (m/M)^2 - (m/M)^3 + ...

Answer 5

now the directions say , use linear correction (no higher orders )

Answer 6

use 1st order correction*

Answer 7

u = m * [ 1 - m/M + (m/M)^2 - (m/M)^3 + ...
1st order correction
u ~ m * ( 1 - m/M)

Answer 8

is it possible you can take a screen shot of the question, sometimes seems odd

Answer 9

is that the letter mu, not u

Answer 10

Yes, is is mu, not u

Answer 11

this was a problem I got in class, I can't take a picture of it