The Bohr Model of the hydrogen atom proposed that there were very specific energy states that the electron could be in. These states were called stationary orbits or stationary states. Higher energy states were further from the nucleus. These orbits were thought to be essentially spherical shells in which the electrons orbited at a fixed radius or distance from the nucleus. The smallest orbit is represented by n=1, the next smallest n=2, and so on, where n is a positive integer representing the shell or orbit. What is the radius of the n=3 orbit for Hydrogen (Z=1)?

R₃ = 4.77 x 10⁻¹⁰ m = 0.477 nm

Explanation:

In 1913, Neil Bohr proposed an atomic model theory, based upon Quantum theory of radiation. This theory described the atomic structure, removing the defects of Rutherford's Model.

In this theory Bohr also derived the formula for the radius of nth orbit of hydrogen atom. The formula is as follows:

Rn = n²(0.53 x 10⁻¹⁰) m

Where,

Rn = Radius of nth orbit of hydrogen atom

n = no. of orbit

Therefore, for 3rd orbit

n = 3

R₃ = (3)²(0.53 x 10⁻¹⁰) m

R₃ = 4.77 x 10⁻¹⁰ m = 0.477 nm

magnityde and direction

i think it because equal matrices have equal dimensions, only square matrices can be symmetric. for all indices and . every square diagonal matrix is symmetric, since all off-diagonal elements are zero. in linear algebra, a real symmetric matrix represents a self-adjoint operator over a real inner product space.