Question

Calculate the orbital bohr radius of the excited state in a hydrogen atom.

O 0.243 nm
O 0.169 nm
O 0.106 nm
O 0.212 nm

Answer 1

The orbital Bohr radius of the excited state in a hydrogen atom for the n=2 level is calculated using the formula rn = n² * a0, resulting in a radius of approximately 0.212 nm.

option d is the correct

Step-by-step explanation:

To calculate the orbital Bohr radius of the excited state in a hydrogen atom, one must consider the quantized nature of electron orbits in a hydrogen-like atom. According to Bohr's model, the sizes of circular orbits for hydrogen-like atoms are given by the radius rn = n² * a0, where n is the principal quantum number indicating the energy level or excited state, and a0 is the Bohr radius constant equal to 5.292 x 10-11 m.

For the first excited state (n=2), the calculation of the orbital radius would be rn = 2² * (5.292 x 10-11 m), which equals 4 * 5.292 x 10-11 m. This results in an orbital radius of 2.1168 x 10-10 m, or 0.21168 nm, which rounds to approximately 0.212 nm.

Therefore, the correct size of the orbital Bohr radius of the excited state in a hydrogen atom to select from the given options is 0.212 nm.