Question

for electromagnetic waves traveling in a vacuum, we can substitute $\frac{c}{\lambda}=f$ for frequency and calculate energy in terms of wavelength.
$e = hf = \frac{hc}{\lambda}$
plancks constant is $6.626×10^{-34}$ joule - seconds (j·s). the speed of light in a vacuum is $2.998×10^{8}$ meters per second.
complete the table to determine the energy carried by each electromagnetic wave traveling in a vacuum.
write your answers in scientific notation rounded to two decimal places.

Explanation:

Step1: Calculate energy for infrared wave

Use the formula \(E=\frac{hc}{\lambda}\).
Substitute \(h = 6.626\times10^{-34}\space J\cdot s\), \(c = 2.998\times 10^{8}\space m/s\), \(\lambda=3.74\times 10^{-4}\space m\)

$$
LATEXBLOCK0
$$

Step2: Calculate energy for visible light

Substitute \(h = 6.626\times10^{-34}\space J\cdot s\), \(c = 2.998\times 10^{8}\space m/s\), \(\lambda = 4.92\times 10^{-7}\space m\)

$$
LATEXBLOCK1
$$

Step3: Calculate energy for X - ray

Substitute \(h = 6.626\times10^{-34}\space J\cdot s\), \(c = 2.998\times 10^{8}\space m/s\), \(\lambda=1.08\times 10^{-10}\space m\)

$$
LATEXBLOCK2
$$

Answer:

Electromagnetic wave	Wavelength (m)	Energy (J)
Visible light	\(4.92\times 10^{-7}\)	\(4.04\times 10^{-19}\)
X - ray	\(1.08\times 10^{-10}\)	\(1.84\times 10^{-16}\)