Question

A dinegative ion of an element has protons whose mass is equal to 14,696 times that of an electron. The number of neutrons is more than the number of protons by 2 . What could be the mass number?

• A. 16
• B. 8
• C. 18
• D. 10

Answer 1

The correct option is C

18

Atomic number (Z) - Atomic number of an element is equal to the number of protons of that element.

Mass number (A) - It is defined as the sum of the protons and neutrons of the element.

Mass of 1 proton, m_p ​=1.67×10⁻²⁷kg

Mass of 1 electron, m_e ​= 9.11×10⁻³¹kg

The explanation for the correct option: (c)

1. Let the dinegative ion be X^2-.
2. The number of electrons, e = number of protons (p) - 2
3. The number of neutrons, n = number of protons (p) +2
4. Now, Mass of protons =14696$\times$m_e

$\mathrm{Total}\mathrm{Mass}\mathrm{of}\mathrm{protons}=14,696\times (9.11\times {10}^{-31}\mathrm{kg})=1.34\times {10}^{-26}\mathrm{kg}$

5. Number of protons is calculated as-

$$\begin{gathered} \mathrm{Number}\mathrm{of}\mathrm{protons}=\frac{\mathrm{Total}\mathrm{mass}\mathrm{of}\mathrm{protons}}{{\mathrm{m}}_{\mathrm{p}}} \\ =\frac{1.34\times {10}^{-26}\mathrm{Kg}}{1.67\times {10}^{-27}\mathrm{kg}} \\ \therefore \mathrm{Number}\mathrm{of}\mathrm{protons}=8 \end{gathered}$$

6. Hence, number of neutrons = 8+2 = 10

7. Finally,

$$\begin{gathered} \mathrm{Mass}\mathrm{number}=\mathrm{number}\mathrm{of}\mathrm{protons}+\mathrm{number}\mathrm{of}\mathrm{neutrons} \\ =8+10 \\ =18 \end{gathered}$$

8. Hence, the mass number of the element = 18.

The correct option is (c).