Question

Find the radius of a hydrogen atom in the (n=2) state according to Bohr's theory.

a) (0.265 , {nm})
b) (0.529 , {nm})
c) (1.058 , {nm})
d) (2.116 , {nm})

Answer 1

The radius of a hydrogen atom in the n=2 state according to Bohr's theory is found by squaring the principal quantum number n and multiplying it by the Bohr radius (0.529 nm). For n=2, the radius is 2.116 nm, corresponding to option (d).

Step-by-step explanation:

To find the radius of a hydrogen atom in the n = 2 state according to Bohr's theory, we use the formula that states the orbital radius is proportional to n². The Bohr radius aB is given to be 0.529 x 10−10 m (0.529 nm) for the n = 1 orbit.

Thus, for n = 2, we square the principal quantum number n to get 2² = 4 and multiply it by the Bohr radius. This gives us the radius for the n = 2 state:

rn=2 = 4 x 0.529 x 10−10 m = 2.116 x 10−9 m

Therefore, the radius of a hydrogen atom in the n = 2 state, according to Bohr's theory, is 2.116 nm, which corresponds to option (d).