Question

Specific heat of water is 4.2 $J/g^{\circ }C$ . If light of frequency 3 x ${10}^9$ Hz is used to heat 400 gm of water from ${20}^{\circ }C$ to ${40}^{\circ }C$ the number of photons needed will be

• A. $1.69\times {10}^{29}$
• B. $1.68\times {10}^{28}$
• C. $2.80\times {10}^4$
• D. $2.80\times {10}^5$

Answer 1

The correct option is B $1.68\times {10}^{28}$

$C=4.2$

$f=3\times {10}^{9}Hz$

$m=400gm$

energy required

$E=mc\left(\Delta T\right)=400\times 4.2\times 20=33600J$

each photon energy $=hv=6.623\times {10}^{-34}\times 3\times {10}^9=19.9\times {10}^{-25}J$

$no.ofphoton=\frac{33600}{19.9\times {10}^{-25}}=1.68\times {10}^{28}$

Hence,

option $\left(B\right)$ is correct answer.