Question

Two fast moving particles X and Y are associated with de Broglie wavelengths 1 nm and 4 nm respectively. If mass of X is nine times the mass of Y, the ratio of kinetic energies of X and Y would be

• A. 3 : 1
• B. 9 : 1
• C. 5 : 12
• D. 16 : 9

Answer 1

Answer: (D)

16 : 9

Answer 2

Given :
$\lambda=\frac{h}{mv}$
Now, $\frac{\lambda_2}{\lambda_1}=\frac{m_1v_1}{m_2v_2}=\frac{4}{1}$
$=\frac{9\times v_2}{1\times v_1}$
$\frac{v_2}{1}=\frac{9}{4}$
K. E = 12 mv2
Now, Ratio of K.E is :
$\frac{K.E_1}{K.E_2}=\frac{16}{9}$
So, the correct option is (D) : 16 : 9.