The radius of an orbit of hydrogen atom is 0.85 nm, then calculate thevelocity of electron in this orbit ?

To calculate the velocity of an electron in an orbit, we can use the formula for the velocity of an electron in a Bohr orbit:

v = e^2/(2ε₀hn)

where:

• e is the elementary charge (1.602 x 10^-19 C)
• ε₀ is the permittivity of free space (8.85 x 10^-12 C^2/N*m^2)
• h is Planck's constant (6.626 x 10^-34 J*s)
• n is the principal quantum number

For a hydrogen atom in its ground state, n = 1.

However, we need to adjust the radius to match the given value. The radius of a Bohr orbit is given by:

r = ε₀h^2n^2/(πme^2)

where m is the electron mass (9.11 x 10^-31 kg).

Solving for n, we get:

n = sqrt(rπme^2/(ε₀h^2))

Substituting the given radius (0.85 nm = 0.85 x 10^-9 m), we can calculate n, and then substitute it back into the velocity formula to find the velocity of the electron.