The statement given in the question is that the product of linear momentum and angular momentum in a hydrogen atom, following Bohr's postulates, is proportional to n times x, where n is the orbit number. The value of x is to be determined.


1. Electrons in an atom revolve around the nucleus in certain stationary orbits without emitting radiation.
2. Electrons can only exist in certain specific energy levels or orbits. These orbits are associated with definite energy values.
3. When an electron jumps from a higher energy level to a lower energy level, it emits radiation with a frequency directly proportional to the energy difference between the two levels.


The linear momentum of an electron in an orbit is given by the product of its mass and velocity. The angular momentum is given by the product of the linear momentum and the radius of the orbit. Mathematically, it can be expressed as:

L = mvr

where L is the angular momentum, m is the mass of the electron, v is its velocity, and r is the radius of the orbit.


According to Bohr's postulates, the energy levels in the hydrogen atom are quantized, meaning they can only have certain discrete values. The orbit number, n, represents these energy levels. The energy of an electron in the nth orbit is given by:

E = -13.6/n^2 eV

Since the energy is quantized, the angular momentum and linear momentum must also be quantized. The product of the two, L x p, is proportional to n times x, where x is a constant.


To determine the value of x, we need to find the relationship between the angular momentum and linear momentum. Using the formula for angular momentum, we can write:

L = mvr = (m/n) x

where x represents the constant of proportionality.

Since L x p is proportional to n times x, we can substitute the expressions for L and p:

(m/n) x^2 = n x

Simplifying the equation, we get:

x = 0

Therefore, the correct answer is x = 0. This means that the product of linear momentum and angular momentum is zero, indicating that the angular momentum and linear momentum are not directly related in the hydrogen atom as per Bohr's postulates.