$f = 1.00 times 10^{13}$ Hz

$textbf{Find: }$ Energy carried by 1 mole of photons

The energy of one photon can be calculated using the formula: $E = hf$

Since, we want to know how much energy is carried by 1 mole of photons, hence we use an alternative formula such that:
$E = nhvf$, where $n$ is the number of photons in 1 mole given by the Avogrado’s number = $6.0 time 10^{23}$

Using these we can now calculate $E$, such that:

$$
begin{align*}
E &= nhf \
&= (6.0 times 10^{23}) times (6.626 times 10^{-34} text{ Js}) times (1.00 times 10^{13} text{ Hz}) \
&= 3.98 text{ kJ}
end{align*}
$$

Hence, the energy carried by 1 mole of photons is $boxed{text{3.98 kJ}}$

$f = 8.2 times 10^{14}$ Hz

$textbf{Find: }$ Energy of photon (in eV)

We can calculate the energy of the photon as follows:

$$
begin{align*}
E &= hf \
&= (6.626 times 10^{-34} text{ Js}) times (8.2 times 10^{14} text{ Hz}) \
&= 5.43 times 10^{-19} text{ J} \
text{converting this to eV we have:} \
E &= 5.43 times 10^{-19} text{ J} times dfrac{1 text{ eV}}{1.6 times 10^{-19} text{ J}} \
&= boxed{3.4 text{ eV}}
end{align*}
$$