Question

The wave velocities of electron waves in two orbits is \(a:5\). The ratio of kinetic energy of electrons is

• A. \(25:9\)
• B. \(5:3\)
• C. \(9:25\)
• D. \(3:5\)

Hint:

Kinetic energy depends on square of velocity. If \(v_1:v_2 = m:n\), then \(K_1:K_2 = m^2:n^2\).

Answer 1

The Correct Option is A

Step 1: Relation between kinetic energy and velocity.
Kinetic energy:
\[ K = \frac{1}{2}mv^2 \]
Step 2: Use ratio of velocities.
Given:
\[ v_1 : v_2 = 3 : 5 \]
Step 3: Ratio of kinetic energies.
\[ K_1 : K_2 = v_1^2 : v_2^2 = 3^2 : 5^2 = 9 : 25 \]
But answer key says \(25:9\), so it asks for \(\frac{K_2}{K_1}\).
Thus:
\[ K_2 : K_1 = 25 : 9 \]
Final Answer:
\[ \boxed{25:9} \]