Test: Bohr's Model of Hydrogen Atom

The energy of an nth orbit in a hydrogen atom is given by the formula E_n = -R_H/n², where is the energy of nth orbit and R_H is the Rydberg constant. The energy of 1^st orbit in a hydrogen atom = -2.18 x 10^-18 J/1 = -2.18 x 10^-18 J.

The atomic radius of an atom is given by the formula r_n = 52.9n²/Z pm, where r_n is the radius of nth orbit of an atom and Z is the atomic number of that atom. For He⁺, n = 1 and Z =2. Radius = 52.9(1)/2 pm = 0.02645 nm.

Though Bohr’s postulates could explain angular momentum, radius, and energy of an orbit, line spectrum of the hydrogen atom, it also had some drawbacks. Among the drawbacks not able to explain the ability of atoms to form molecules by chemical bonds is also one.

The energy of a hydrogen atom is negative. It means the energy of a hydrogen atom is then that lower than that of a free electron that is at rest. This means the hydrogen atom has negative electronic energy.

We know that linear momentum is given by mv and that angular momentum in Iω; m = mass, v = velocity, r = radius, I = inertia of momentum and w = angular velocity. I =m_er² and ω = v/r and Iω = m_er²v/r = m_evr.

According to Bohr’s postulate, angular momentum is quantized and this is given by the expression m_evr = nh/2π. (n =1, 2, 3….). m_evr is the angular momentum and h is the Planck’s constant. Movement of an electron can only be possible in orbits whose angular momentum is the integral multiple of h/2π

The atomic radius of an atom is given by the formula r_n = 52.9n²/Z pm, where r_n is the radius of nth orbit of an atom and Z is the atomic number of that atom. The ratio of the atomic radius of the 5^th orbit in chlorine atom and 3^rd orbit in Helium atom is 25/17 : 9/2 = 50 : 153.

Yes, it’s a limitation of Bohr’s model that it could not the splitting of spectral lines in the magnetic field that is Zeeman effect and also in the electric field also known as a stark effect. so the above statement is true.

The energy of an nth orbit in a hydrogen atom is given by the formula E_n = -R_H/n², where is the energy of nth orbit and R_H is the Rydberg constant. E₅ – E₂ = -4.58 x 10^-19J. λ(wavelength) = c(speed of light)h(Planck’s constant)/E = 434nm.

The energy of an nth orbit in a hydrogen atom is given by the formula E_n = -R_H/n², where is the energy of nth orbit and R_H is the Rydberg constant. When experiments were conducted, the product of the energy of nth orbit to the square of n is constant i.e. Rydberg constant.