Question

In Bohr's model of the hydrogen atom, which of the following pairs of quantities are quantized?

• A. Energy and linear momentum
• B. Linear and angular momentum
• C. Energy and angular momentum
• D. None of the above

Answer 1

Answer: (C)

According to Bohr's theory of atom electrons can revolve only in those orbits in which their angular momentum is an integral multiple of $\frac{h}{2\pi }$ , where $h$ is Planck's constant.
Angular momentum $=mvr=\frac{2h}{2\pi }$
Hence, angular momentum is quantized.
The energy of electron in $n$ th orbit of hydrogen atom,
$E=$ $\frac{Rhc}{n^2}$ joule
Thus, it is obvious that the hydrogen atom has some characteristics energy state. In fact this is true for the atom of each element, $ie,$ each atom has its energy quantized.
Hence, both energy and angular momentum are quantized.