The radii of the Bohr orbits in atomic hydrogen are given by If the radius of the first Bohr orbit (n = 1)is 0.053 nm,the radius of the third Bohr orbit (n = 3)is
A)0.16 nm
B)0.018 nm
C)0.48 nm
D)0.35 nm
E)1.3 nm

Question

The radii of the Bohr orbits in atomic hydrogen are given by  If the radius of the first Bohr orbit (n = 1)is 0.053 nm,the radius of the third Bohr orbit (n = 3)is
A)0.16 nm 
B)0.018 nm 
C)0.48 nm 
D)0.35 nm 
E)1.3 nm

Quizplus · Accepted Answer

Given, the formula for the radius of the Bohr orbit is given by r = (0.529 × n^2) / Zangstrom, where n is the principal quantum number and Z is the atomic number. 
Using this formula for n = 1, we get:
r1 = (0.529 × 1^2) / 1angstrom = 0.529angstrom = 0.053 nm
For n = 3, we have:
r3 = (0.529 × 3^2) / 1angstrom = 4.761angstrom = 0.4761 nm
Therefore, the radius of the third Bohr orbit is 0.48 nm (option C).

The Radii of the Bohr Orbits in Atomic Hydrogen Are