What is the specific charge of a $^{13}_{6}C$ nucleus? A 4.4 × 10¹⁷ C kg⁻¹ B 5.2 × 10¹⁷ C kg⁻¹ C 8.3 × 10¹⁷ C kg⁻¹ D 2.1 × 10¹⁸ C kg⁻¹ - AQA - A-Level Physics - Question 10 - 2022 - Paper 1

To calculate the specific charge of a nucleus, we need to determine its charge and mass.

1. Determine the number of protons and neutrons in $^{13}_{6}C$:

   • The atomic number (6) indicates there are 6 protons.
   • The mass number (13) indicates there are 13 - 6 = 7 neutrons.

2. Calculate the charge of the nucleus:

   • The charge of one proton is approximately +1.6 x 10^{-19} C.
   • Therefore, the total charge of the $^{13}_{6}C$ nucleus is:

   $Q = 6 imes (1.6 imes 10^{-19}) = 9.6 imes 10^{-19} ext{ C}$

3. Determine the mass of the nucleus:

   • The approximate mass of a carbon nucleus is about 13 atomic mass units (u).
   • Converting atomic mass units to kilograms: 1 u = 1.66 x 10^{-27} kg.
   • Therefore, the mass is:
   = 2.158 imes 10^{-26} ext{ kg} $$

4. Calculate the specific charge:

   • The specific charge (SC) is defined as charge per unit mass:
   \ = 4.44 imes 10^{7} ext{ C kg}^{-1} $$

Thus, the specific charge of a $^{13}_{6}C$ nucleus is approximately 4.4 × 10¹⁷ C kg⁻¹.