Answer
Infrared $253.546\times10$$^2$$^1$ photons
Blue light $198.611\times10$$^1$$^9$ photons
Work Step by Step
Given
Mass $(m)$$=$ $0.50kg$
Specific heat capacity glass $($$c_°$$)$$=$$840j/kg C^°$
Infrared light wavelength$($$\lambda_l$$)$$=6\times10$$^-$$^5$$m$
Blue light wavelength$($$\lambda_b$$)$$=4.7\times10^-$$^7$$m$
Rise in temperature$($$\Delta$$T)$$=2$ $^°C$
As we know
$Q=mc_°$$\Delta$$T$
Here $Q$ is heat energy which can be written as
$nhc/$$\lambda$ where $n$ is the number of photons.
$nhc/$$\lambda$$=mc_°$$\Delta$$T$
$n=$$($$mc_°$$\Delta$$T$$/$$hc$ $)$$\times$$\lambda$
For infrared light
$n=$ $($$0.5\times840\times2$$)/$$($$6.626\times10$$^-$$^3$$^4$$\times3\times10$$^8$$)$ $\times6\times10$$^-$$^5$
$n=253.546\times10$$^2$$^1$photons
And similarly for blue light
$n=$$($$0.5\times840\times2\times4.7\times10$$^-$$^7$$)$$\div$$(6.626\times10$$^-$$^3$$^4$$\times3\times10$$^8$$)$
$n=198.611\times10$$^1$$^9$photons
