Calculate the value of the constant N in the given radial function when this radial function
is normalized. The radial function is defined as follows:
R(r)= Nr’e-ar?
Here, N is the normalized constant and a is the positive constant.
1
1
(A)
3/2
a
45
2
(B)
3/2
a
Vr
a
1
(C)
,32
(
2W
1
(D)
(32
Answers
Answered by
0
The value of the constant N when the radial function is normalized is given by option (C) N = sqrt(a^3/2).
Given:
Radial function R(r) = Nr'e^(-ar)
To Find:
the value of the constant N after normalizing the radial function.
Solution:
The normalized radial function is defined as follows:
∫(0 to ∞) |R(r)|^2 r^2 dr = 1
Substituting R(r) in the above equation, we get:
∫(0 to ∞) |Nr'e^(-ar)|^2 r^2 dr = 1
=> N^2 ∫(0 to ∞) r^2 e^(-2ar) dr = 1
Using the formula ∫(0 to ∞) x^n e^(-ax) dx = n!/a^(n+1), we get:
N^2 * 2!/a^3 = 1
=> N = sqrt(a^3/2)
Therefore, the value of the constant N when the radial function is normalized is given by option (C) N = sqrt(a^3/2).
#SPJ1
Similar questions