Concept:Equivalent Dose (\(D_e\)) measures the biological effect of radiation, calculated by multiplying the Physical Dose (\(D\)) by the Relative Biological Effectiveness (RBE). Physical Dose is the absorbed energy per unit mass.
Formula:$$ D_e = D \times \text{RBE} $$
$$ D = \frac{E}{m} $$
Solution:- Given: \(D_e = 400\text{ rem}\), \(\text{RBE} = 10\), \(m = 80\text{ kg}\).
- First, convert rem to standard SI units (Sieverts): $$ 1\text{ Sv} = 100\text{ rem} \implies 400\text{ rem} = 4\text{ Sv} $$
- Calculate Physical Dose (\(D\)): $$ D = \frac{D_e}{\text{RBE}} = \frac{4}{10} = 0.4\text{ Gy (or J/kg)} $$
- Calculate Total Energy (\(E\)): $$ E = D \times m = 0.4\text{ J/kg} \times 80\text{ kg} = 32\text{ J} $$
Why other options are incorrect:Option A results from forgetting to convert rem to Sieverts properly or dividing by 2. Options C and D are arithmetic errors in multiplication.
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