Question

If at a certain location in space, the wave function ψ of an electron has a numerical value of 0.2, the probability density at that point of space should be:

0.1

0.04

0.8

0.2

0.4

For a first order reaction with one reactant, the initial concentration of the reactant is 2.0 M and the rate constant k is 2 M/s, the half-life should be (in s):

0.347

0.693

0.25

1.0

4.0

Answer 1

1. The formula of probability density p at a point given by :

p = |ψ|^2

where ψ is the wave function at that location

=> p = (0.2)^2

=> p = 0.04

Hence, option-2 i e, 0.04 is the correct answer.

2. Note : In this question, the reaction is first order. The units of rate constant for the first order reaction is sec^-1 and not M/sec. Hence, k should be 2 sec^-1.

Given : Initial concentration, [Ao] = 2.0 M

Rate constant, k = 2 s^-1

For the first order reaction, half life, t_{​​​​​1/2} is given by:

t_{​​​​​1/2} = 0.693/k

=>  t_{​​​​​1/2} = 0.693/2 s^-1 = 0.347 s

Hence, option-1 i.e, 0.347 is the correct answer.