Question

Find the number of quanta of radiations of frequency $5.03\times {10}^{13}{\text{s}}^{-1}$ that must be absorbed in order to melt 5 g of ice. The energy required to melt 1 g of ice is 333 J.

• A. $5.38\times {10}^{23}$
• B. $6.52\times {10}^{22}$
• C. $5.00\times {10}^{22}$
• D. $6.37\times {10}^{22}$

Answer 1

The correct option is C $5.00\times {10}^{22}$

Given,
energy required to melt 1 g of ice $=333J$
So, energy required to melt 5 g of ice $=5\times 333J=1665J$
Again, energy associated with one quantum $=hv$
$=(6.62\times {10}^{-34})\times (5.03\times {10}^{13})=33.298\times {10}^{-21}J$
$\approx 33.30\times {10}^{-21}J$
The number of quanta required to melt 5 g of ice
$=\frac{1665}{33.30\times {10}^{-21}}=50\times {10}^{21}=5.0\times {10}^{22}$