Question

If potential energy between a proton and an electron is given by |U|=ke2/2R3, where e is the charge of electron and R is the radius of atom, then radius of Bohr's orbit is given by (h = Planck's constant, k = constant)

A. ke²m/h²
B. 6π²ke²m/n² h²
C. 2πke²m/n h²
D. 4π²ke²m/n²h²

Answer 1

The radius of Bohr's orbit, based on the quantized angular momentum proposed by Bohr and the constants provided in the quantum theory of atomic orbitals, is best represented by option D. 4π²ke²m/n²h².

Step-by-step explanation:

The question assesses the understanding of Bohr's model of the hydrogen atom and involves the application of the formula concerning the quantum theory of atomic orbitals. By Bohr's theory, the quantized orbital angular momentum is given by L = n(h/2π), where 'n' is the principal quantum number and 'h' is Planck's constant.

Also, according to the formula Bohr derived, the radius of the nth orbit for a hydrogen-like atom is given by rn = (n² × h²) / (4π² × me × k × e²), where 'me' is the electron's mass, 'k' is Coulomb's constant, and 'e' is the charge of the electron.

To find the correct expression for the radius of Bohr's orbit from the provided options, we can simply rearrange the formula:

rn = n² × (h² / (4π² × me × k × e²)).

Hence, the correct answer is D. 4π²ke²m/n²h².