Question

$A^{x+}$ has $4$ protons, $5$ neutrons and $e/m$ value of $2.12\times {10}^7{\text{C kg}}^{-1}$. Find the value of $x$.

• A. $1$
• B. $2$
• C. $3$
• D. $4$

Answer 1

The correct option is B $2$

Charge/mass value for $A^{x+}=2.12\times {10}^7{\text{C kg}}^{-1}$
Since, $A^{x+}$ has 4 protons and 5 neutrons and the mass of a proton is approximately equal to the mass of a neutron. The effective mass of the ion will be approximately equal to $9m_p$ where $m_p$ is the mass of a proton
Mass of $A^{x+}=9\times 1.67\times {10}^{-27}\text{kg}=1.503\times {10}^{-26}\text{kg}$
Also $A^{x+}$ has +x relative charge.
Charge of $A^{x+}=x\times e=x\times 1.602\times {10}^{-19}$ C
The value of charge to mass ratio for the ion will be given by
$2.12\times {10}^7{\text{C kg}}^{-1}=\frac{x\times 1.602\times {10}^{-19}C}{1.503\times {10}^{-26}\text{kg}}$

$\Rightarrow x=2$