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

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

NTA AbhyasNTA Abhyas 2020Atoms

Solution:

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 $=mvr=\frac{2 h}{2 \pi }$
Hence, angular momentum is quantized.
The energy of electron in $n$ th orbit of hydrogen atom,
$ \, \, \, E \, =$ $\frac{R h c}{n^{2}}$ 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.