Question

Which of the following suggested de-Broglie wavelength(s) is/ are possible for electron in a Bohr orbit of hydrogen atom?

• A. $19.92A$
• B. $9.96A$
• C. $4.98A$
• D. $3.32A$

Answer 1

Answer: (D)

$3.32A$

By De-Broglie Equation, $\lambda =\frac{h}{mv}$.....(1)
Planks Constant, $h=6.626\times 10^{-34}Js$
mass of electron, $m=9.1\times 10^{-31}Js$
velocity of electron in first orbit of hydrogen atom, $v=2.18\times 10^{6}m/s$
$mv=9.1\times 10^{-31}\times 2.18\times 10^{6}m/s=1.9838\times 10^{-24}m/s$
putting values in equation 1,
$\lambda =\frac{6.626\times 10^{-34}}{1.9838\times 10^{-24}}=3.3400\times 10^{-10}m=3.3400A$
Conclusion= hence the option (C) is correct.