Question

$A^{x+}$ has 4 protons, 5 neutrons and e/m value of $2.12\times {10}^7$ C/kg. 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
Value of charge by mass for the ion will be given by
$2.12\times {10}^7{\text{C kg}}^{-1}=\frac{x\times 1.602\times {10}^{-19}C}{1.503\times {10}^{-26}\text{kg}}$

$\Rightarrow x=2$