From the given information, the angular momentum of the electron is L = 6.834 × 10^(-34) J·s.
We also have the equation L = sqrt(l(l+1)) * h/(2*pi). We can solve for l using this equation:
6.834 × 10^(-34) = sqrt(l(l+1)) * (6.626 × 10^(-34))/(2*pi)
-> l(l+1) = ((6.834 × 10^(-34))*2*pi/(6.626 × 10^(-34)))^2
Now, calculate the value of l(l+1):
l(l+1) ≈ 1.066
-> l^2 + l - 1.066 = 0
This quadratic equation doesn't have an integer solution for l. But we know that l can only be integer values (0, 1, 2, ...). Since 0 wouldn't satisfy the equation, the closest integer value for l is 1.
Now that we know the value for l, we can find the largest possible value for the z-component of the angular momentum (Lz). For a given l, the maximum value of Lz occurs when ml = l. Therefore, the largest value of Lz can be found using:
Lz_max = ml*h/2*pi
= l * h/2*pi
= 1 * (6.626 × 10^(-34))/(2*pi)
Lz_max ≈ 5.272 * 10^(-34) J·s
The electron in a certain hydrogen atom has an angular momentum of 6.834 × 10-34 J·s. What is the largest possible magnitude for the z component of the angular momentum of this electron? For accuracy, use h = 6.626 × 10-34 J·s.
I know you need to use the equations Lz=ml* h/2*pi
then use L=sqrt of l(l+1) times h/2pi
not sure where to go from here
1 answer
1 answer