Question

Use Bohr's model of the H atom to explain the origin and the characteristics of X-rays.

Answer 1

According to Bohr's model of hydrogen atom,the hydrogen atom is explained as a positively charged nucleus (wirh only one proton and no neutron) . This nucleus is surrounded by negatively charged electrons(only one in case of hydrogen). These two oppositely charged particles are kept together by electrostatic force between them.

Bohr corrected Rutherford by stating that every electron can have a stable orbit around the nucleus without radiating any electromagnetic radiation. He postulated that electrons are orbiting around the nucleus in specific shells. Each shell has a specific energy associated with it. He expressed these shells in terms of principal quantum number 'n'. Higher values of n correspond to increasing energy. The orbits are termed as k,l,m,n (corresponding to n=1,2,3,4 respectively).

The inner shell electrons (k,l) have higher ionisation energy than outer shell electrons because the binding energy (energy required to knock the electron out of the orbit varies inversely with n).

That means higher amount of energy is needed to knock a k shell electron out of its orbit. Bohr also postulated that it is possible for an electron to jump to a higher energy level or a lower energy level. So every time a k shell electron is knocked out of it's orbit,an 'l' shell electron comes down to the k shell, filling up the vacancy in k shell. While doing this the l shell electron emits energy equal to the energy difference between k and l shell. This energy is released in the form of electromagnetic radiation.This energy is related to the frequency of electromagnetic radiation as .

Whenever the transition occurs in the inner shells,a very high amount of energy is released in the form of high frequency, low wavelength electromagnetic radiation called x rays.

An important characteristic of x rays is their spectrum. Each element has a different distribution of energy levels. That means each element has its own characteristic spectrum of x rays, specific to that element only.

Another characteristic of x rays is the extremely high energy which is a result of the fact that x rays are produced due to inner electronic transitions. These electrons are very tightly bound and thus have a high binding energy. So they require a high ionisation energy as well.

X rays created by bombarding a target by high energy particles have a continuous spectrum and as we increase the energy of bombarding particles the spectral curves shift towards lower wavelengths i e. Higher energy x rays . This can be explained by .

The transitions from second shell to first shell are called k-alpha transitions while the transitions from third shell to first shell are called k-beta transitions. The x ray characteristic spectrum has its highest values at this two transitions. The fact that the x ray characteristic spectrum is continuous rather than discrete suggests that there are other energy levels in between these shells.

X rays are extremely monochromatic. But the characteristic x ray spectrum is not monochromatic in the strict sense. It is polychromatic to some extent. It is therefore called white radiation or bremsstrahlung ( breaking radiation) . If we choose a specific wavelength from this spectrum we can get a highly monochromatic x ray beam