In a mass spectrometer used for measuring the masses of ions, the ions are initially accelerated by an electric potential V and then made to describe semicircular paths of radius R using a magnetic field B. If V and B are kept constant, the ratio (( text Charge on the ion / text mass of the ion )) will be proportional to:-

Question

In a mass spectrometer used for measuring the masses of ions, the ions are initially accelerated by an electric potential V and then made to describe semicircular paths of radius R using a magnetic field B. If V and B are kept constant, the ratio (( text Charge on the ion / text mass of the ion )) will be proportional to:- (A) 1/R2 (B) R2 (C) R (D) (1/ R )

Tardigrade Admin · Accepted Answer

Radius of semicircular path R =( mv / qB )=(√2 mqV / qB ) As V and B are constant so R α (√ mq / q ) ⇒ ( q / m ) propto (1/ R 2)

$1/ R^{2}$

$R^{2}$

$R$

$\frac{1}{R}$

Radius of semicircular path
$R = \frac{m v}{qB} = \frac{2 m q V}{qB}$
As $V$ and $B$ are constant so
$R α \frac{m q}{q}$
$\Rightarrow \frac{q}{m} \propto \frac{1}{R ^{2}}$

1/R2

R2

R

R1​

Radius of semicircular path R=qBmv​=qB2mqV​​ As V and B are constant so Rαqmq​​ ⇒mq​∝R21​

$1/ R^{2}$

$R^{2}$

$R$

$\frac{1}{R}$

Radius of semicircular path
$R = \frac{m v}{qB} = \frac{2 m q V}{qB}$
As $V$ and $B$ are constant so
$R α \frac{m q}{q}$
$\Rightarrow \frac{q}{m} \propto \frac{1}{R ^{2}}$