The radius of the innermost electron orbit of a hydrogen atom is5.3×10–11 m. What are the radii of the n = 2 and n =3 orbits?

To find the radii of the n = 2 and n = 3 orbits of a hydrogen atom, we can use the formula for the radius of an electron orbit in the Bohr model. The formula is given by:

r = (0.529 × n^2) / Z

where r is the radius of the orbit, n is the principal quantum number, and Z is the atomic number (which is 1 for hydrogen).

For the n = 2 orbit, we can substitute n = 2 and Z = 1 into the formula:

r = (0.529 × 2^2) / 1 r = (0.529 × 4) / 1 r = 2.116 / 1 r = 2.116

Therefore, the radius of the n = 2 orbit is approximately 2.116 × 10^-10 m.

Similarly, for the n = 3 orbit, we substitute n = 3 and Z = 1 into the formula:

r = (0.529 × 3^2) / 1 r = (0.529 × 9) / 1 r = 4.761 / 1 r = 4.761

So, the radius of the n = 3 orbit is approximately 4.761 × 10^-10 m.