Explain the construction and working of a Bainbridge mass spectrometer. Mention its use.

The Bainbridge mass spectrometer is an instrument designed to measure the atomic masses of isotopes of any element with the highest level of accuracy.

A Bainbridge mass spectrometer primarily consists of a discharge tube that generates ions. The discharge tube emits a beam of positive ions into a tube. These ions are formed when one or more electrons are removed from an atom. The tube is equipped with two slits, S₁ and S₂, which help collimate the ion beam.

The beam then passes through a velocity selector, which allows only particles with a specific velocity to pass through. This selection is achieved by the combined action of a magnetic field and an electric field, arranged perpendicular to each other. The electric field is applied using two plates, P₁ and P₂, while the magnetic field is denoted as B. The perpendicular arrangement ensures that the effects of the fields cancel out, preventing any deflection of the particles.

Forces Acting on the Particle

• Magnetic force:F_m = q B v, where q is the particle’s charge, v is its velocity, and B is the magnetic field.
• Electric force:F_e = q E, where E is the electric field.

Since the forces cancel each other in the velocity selector:

q B v = q E → v = E / B

Thus, only particles with velocity v = E / B pass through the velocity selector.

After passing through a third slit, S₃, the ions enter a vacuum chamber with a strong magnetic field, B′, oriented perpendicular to the plane of motion. This magnetic field causes the particles to move in a circular path, striking a photographic plate at the end. The centripetal force for this motion is given by:

B' q v = m v² / R 

m = B' q R

Variables Explained

• B′ = magnetic field in the vacuum chamber
• q = charge of the particle
• v = velocity of the particle
• m = mass of the particle
• R = radius of the particle’s circular path

By knowing the values of these variables, the mass of the particle can be accurately calculated.