Mass Spectrometry Ion Velocity Derivation

The velocity ($v$) of an ion in mass spectrometry is fundamentally linked to its kinetic energy ($K.E.$) and mass ($m$).

Kinetic Energy Equation

The basic physics formula for kinetic energy is:

$K.E. = \frac{1}{2}mv^2$

Deriving the Velocity Expression

To find the ion velocity ($v$), we rearrange the kinetic energy formula:

1. Isolate $v^2$: Multiply the equation by 2 and divide by $m$.
$v^2 = \frac{2 \times K.E.}{m}$
2. Solve for $v$: Take the square root of both sides, which is equivalent to raising to the power of 0.5.
$v = (\frac{2 \times K.E.}{m})^{0.5}$

This derived expression can be written in the format $v = ((2 \times K.E.) / m)^{0.5}$.

Evaluating Options

We compare this derived formula with the provided options:

• Option 1: $v = ((2.K.E)/m)^{1.5}$ - The exponent (1.5) is incorrect.
• Option 2: $v = ((2.K.E)/m)^{0.5}$ - This matches the derived formula for ion velocity.
• Option 3: $v = ((2.K.E)/m)^2$ - The exponent (2) is incorrect.
• Option 4: $v = ((K.E)/2.m)^{0.5}$ - The factor of 2 is incorrectly placed in the denominator.

Final Determination

Based on the derivation from the kinetic energy principle, the correct expression for ion velocity is $v = ((2 \times K.E.) / m)^{0.5}$.