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

According to the Bohr model, the radii of Bohr orbits in hydrogen are given by the formula:

r_n = (n^2 * h^2 * ε_0) / (π * m_e * e^2)

where n is the principal quantum number (n = 1, 2, 3...), h is Planck's constant, ε_0 is the permittivity of free space, m_e is the mass of the electron, and e is the elementary charge.

Given that the radius of the first Bohr orbit (n = 1) is 0.053 nm, we can use the above formula to find the radius of the third orbit (n = 3):

r_3 = (3^2 * h^2 * ε_0) / (π * m_e * e^2) = 9 * (0.053 nm) = 0.48 nm

Therefore, the correct answer is (C) 0.48 nm.

The Radii of the Bohr Orbits in Atomic Hydrogen Are