Atomic Structure Question 414
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
Options:
A) 3 : 1
B) 9 : 1
C) 5 : 12
D) 16 : 9
Show Answer
Answer:
Correct Answer: D
Solution:
- de Broglie wavelength $ \lambda =\frac{h}{mv} $
$ \frac{{\lambda_1}}{{\lambda_2}}=\frac{m_2v_2}{m_1v_1};\frac{1}{4}=\frac{1}{9}\times \frac{v_2}{v_1} $
$ \frac{v_2}{v_1}=\frac{9}{4};\frac{v_1}{v_2}=\frac{4}{9} $
$ KE=\frac{1}{2}mv^{2} $
$ \frac{KE_1}{KE_2}=\frac{m_1}{m_2}\times \frac{v_l^{2}}{v_2^{2}}=\frac{9}{1}\times {{( \frac{4}{9} )}^{2}}=\frac{16}{9} $
