If the energy of a photon corresponding to a wavelength of $6000 \mathring A$ is $3.32 \times 10^{-19} \ J$,the photon energy for a wavelength of $4000 \mathring A$ will be ............ $eV$.

The radiant energy from the Sun incident on the Earth's surface is $2 \ cal/cm^2 \cdot min$. If the average wavelength of solar radiation is $5500 \ \mathring A$,then the number of photons incident per minute on a surface area of $1 \ cm^2$ on the Earth's surface is ............ $(h = 6.6 \times 10^{-34} \ J \cdot s, 1 \ cal = 4.2 \ J)$

The frequency of a photon having energy $100 \ eV$ is $(h = 6.6 \times 10^{-34} \ J \cdot s)$.

The minimum intensity of light that can be perceived by the human eye is $10^{-10} \ W/m^2$. If the area of the pupil is $10^{-6} \ m^2$ and the wavelength of light is $560 \ nm$,approximately how many photons per second enter the eye? (Use $h = 6.6 \times 10^{-34} \ J \cdot s$ and $c = 3 \times 10^8 \ m/s$).

An electron and a proton are detected in a cosmic ray experiment,the first with kinetic energy $10 \; keV$,and the second with $100 \; keV$. Which is faster,the electron or the proton? Obtain the ratio of their speeds. (Electron mass $= 9.11 \times 10^{-31} \; kg$,proton mass $= 1.67 \times 10^{-27} \; kg$,$1 \; eV = 1.60 \times 10^{-19} \; J$)

There are two sources of light,each emitting with a power of $100 \, W$. One emits $X$-rays of wavelength $1 \, nm$ and the other visible light at $500 \, nm$. Find the ratio of the number of photons of $X$-rays to the photons of visible light of the given wavelength.