Question

Given that Psi(x) = √a*exp(-ax), find the probability of finding a particle between X=1/a and x=2/a. [9 marks]

a) 1/3
b) 1/2
c) 2/3
d) 3/4

Answer 1

To find the probability of finding a particle between X=1/a and x=2/a, we need to calculate the area under the function Psi(x) between these two points. The probability is 1/3.

Step-by-step explanation:

To find the probability of finding a particle between X=1/a and x=2/a, we need to calculate the area under the function Psi(x) between these two points. The probability is given by the integral of |Psi(x)|^2 dx with the limits of integration from 1/a to 2/a. Psi(x) = sqrt(a)*exp(-ax), Psi(x)^2 = a*exp(-2ax), Probability = integral of a*exp(-2ax) dx from 1/a to 2/a. Using the definite integral, we can evaluate this probability to be 1/3. Therefore, the correct answer is a) 1/3