More practice questions

4. Q4. Find (a) the number and (b) the total mass of neutrons in 7 mg of ^¹⁴C, taking the mass of a neutron as 1.675 × 10^⁻²⁷ kg and the molar mass of ^¹⁴C as 14 g mol^⁻¹ (NCERT Exercise 2.2(ii), page 69).

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   7 mg = 7 × 10^⁻³ g, and (7 × 10^⁻³ g) ÷ (14 g mol^⁻¹) = 5.0 × 10^⁻⁴ mol of atoms. Each ^¹⁴C atom has 14 − 6 = 8 neutrons, so there are 8 × 5.0 × 10^⁻⁴ × 6.022 × 10^²³ ≈ 2.409 × 10^²¹ neutrons. Their mass is 2.409 × 10^²¹ × 1.675 × 10^⁻²⁷ kg ≈ 4.035 × 10^⁻⁶ kg (about 4 mg).

5. Q5. Find (a) the number and (b) the total mass of protons in 34 mg of NH₃ (molar mass 17 g mol^⁻¹, proton mass 1.6726 × 10^⁻²⁷ kg). Would the answer change at another temperature and pressure (NCERT Exercise 2.2(iii), page 69)?

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   34 mg = 34 × 10^⁻³ g, and (34 × 10^⁻³ g) ÷ (17 g mol^⁻¹) = 2.0 × 10^⁻³ mol. Each NH₃ has 7 + 3 = 10 protons, so there are 10 × 2.0 × 10^⁻³ × 6.022 × 10^²³ ≈ 1.204 × 10^²² protons, of mass 1.204 × 10^²² × 1.6726 × 10^⁻²⁷ kg ≈ 2.014 × 10^⁻⁵ kg. No: a fixed mass of NH₃ has the same number of protons whatever the temperature and pressure.

6. Q6. How many times as heavy as an electron is a proton? Use NCERT’s masses, 1.6726216 × 10^⁻²⁷ kg and 9.109382 × 10^⁻³¹ kg.

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   (1.6726216 × 10^⁻²⁷ kg) ÷ (9.109382 × 10^⁻³¹ kg) ≈ 1836. A proton is about 1836 times as heavy as an electron.