Question

Let r,v and E are the radius of the orbit, speed of the electron and the total energy of the electron respectively. Which of the following quantities are proportional to the quantum number’n’?

Answer 1

Given: r, v and E are the radius of the orbit, speed of the electron and the total energy of the electron respectively.

To find: Which quantities are proportional to the quantum number ’n’?

             Options: a. vR     b. RE      c. v/E      d.R/E

Solution:

• Now we have given r, v and E are the radius of the orbit, speed of the electron and the total energy of the electron respectively.

• So the velocity of revolving electron is:

             v = e²/2nh∈o

• Now the energy of an electron is:

             E = -me^4/8n²h²∈o²

• Now dividing both, we get:

             v/E = e²/2nh∈o ÷ -me^4/8n²h²∈o²

             v/E = e²/2nh∈o x 8n²h²∈o²/-me^4

             v/E = 4nh∈o/me²

• So v/E ∝ n.

Answer:

          So v/E is proportional to the quantum number ’n’.(c)