Question

q4 7. how much energy is required to produce a wavelength of 1.25×10^16 meters? 1.59×10^41 j 1.77×10^-58 j 1.25×10^23 j 3.45×10^24 j clear all

Explanation:

Step1: Recall the energy - wavelength formula

The formula for the energy of a photon is $E = \frac{hc}{\lambda}$, where $h = 6.626\times10^{- 34}\text{ J}\cdot\text{s}$ (Planck's constant), $c = 3\times10^{8}\text{ m/s}$ (speed of light) and $\lambda$ is the wavelength.

Step2: Substitute the given values

Given $\lambda=1.25\times 10^{16}\text{ m}$, $h = 6.626\times10^{-34}\text{ J}\cdot\text{s}$ and $c = 3\times10^{8}\text{ m/s}$. Then $E=\frac{6.626\times 10^{-34}\times3\times 10^{8}}{1.25\times 10^{16}}$.
First, calculate the numerator: $6.626\times 10^{-34}\times3\times 10^{8}=19.878\times10^{- 26}=1.9878\times10^{-25}\text{ J}\cdot\text{m}$.
Then, divide by the denominator: $E=\frac{1.9878\times 10^{-25}}{1.25\times 10^{16}}$.
Using the rule of exponents $\frac{a\times10^{m}}{b\times10^{n}}=\frac{a}{b}\times10^{m - n}$, we have $E=\frac{1.9878}{1.25}\times10^{-25 - 16}=1.59024\times10^{-41}\text{ J}\approx1.59\times10^{-41}\text{ J}$.

Answer:

$1.59\times 10^{-41}\text{ J}$