Answer:
a
[tex]n = 23[/tex]
b
[tex]v = 87377.95 \ m/s[/tex]
Explanation:
From the question we are told that
The diameter is [tex]d = 61\ nm = 61 *10^{-9} \ m[/tex]
Generally the radius electron orbit is mathematically represented as
[tex]r = \frac{61 *10^{-9}}{2}[/tex]
=> [tex]r = 3.05*10^{-8} \ m[/tex]
This radius can also be represented mathematically as
[tex]r = n^2 * a_o[/tex]
Here n is the quantum number and [tex]a_o[/tex] is the Bohr radius with a value
[tex]a_o = 0.0529 *10^{-9} \ m[/tex]
So
[tex]n = \sqrt{\frac{3.05*10^{-8}}{ 0.059*10^{-9}} }[/tex]
=> [tex]n = 23[/tex]
Generally the angular momentum of the electron is mathematically represented as
[tex]L = m * v * r = \frac{n * h }{2 \pi}[/tex]
Here h is the Planck constant and the value is [tex]h = 6.626*10^{-34} J \cdot s[/tex]
m is the mass of the electron with values [tex]m = 9.1*10^{-31} \ kg[/tex]
So
[tex]v = \frac{23 * 6.626*10^{-34} }{2\pi * 9.1 *10^{-31} * 3.05*10^{-8} }[/tex]
[tex]v = 87377.95 \ m/s[/tex]
