The half life of a radioactive substance is 10 years and its initial mass is 1 g. The remaining amount after 20 years is ________.

Correct option is C

​$$\text{Given:} \\\text{Half-life } t_{1/2} = 10 \, \text{years} \\\text{Initial mass } N_0 = 1 \, \text{g} \\\text{Time } T = 20 \, \text{years}$$

$$N = \frac{N_0}{2^n} \\\text{Where } N_0 \text{ is the initial mass and } n \text{ is the number of half-lives.} \\n = \frac{\text{Total time}}{\text{Half-life}} = \frac{T}{t_{1/2}} \\\text{Put all given values in the formula, we get:} \\n = \frac{T}{t_{1/2}} = \frac{20}{10} = 2 \, \text{years} \\\text{Now, using the formula for remaining mass:} \\N = \frac{1}{2^2} = \frac{1}{4} = 0.25 \, \text{g}$$​​​