Question

the atomic emission spectrum for a particular element includes blue - violet light with wavelength 440. nm. calculate the energy in joules of this light given that e = h c/λ, and h = 6.63 x 10^(-34) js, and c = 3.00 x 10^8 m/s. (h and c are constants, λ is wavelength, convert nm into m)

h c 1 2

e = ---- =---------------- = 3

λ 4

a. 6.63 x 10^(-34) js b. 3.00 x 10^8 m/s c. 440. nm d. 440. x 10^(-9) m

e. 4.52 x 10^(-28) j f. 4.52 x 10^(-19) j

Explanation:

Step1: Convert wavelength to SI unit

We know that $1\ nm = 10^{-9}\ m$, so $\lambda=440\ nm = 440\times10^{-9}\ m$.

Step2: Substitute values into formula

Given $h = 6.63\times 10^{-34}\ Js$ and $c = 3.00\times 10^{8}\ m/s$, and $\lambda = 440\times 10^{-9}\ m$, we use the formula $E=\frac{hc}{\lambda}$.
$E=\frac{6.63\times 10^{-34}\times3.00\times 10^{8}}{440\times 10^{-9}}$

Step3: Calculate the energy

$E=\frac{6.63\times3.00}{440}\times10^{-34 + 8+9}=\frac{19.89}{440}\times10^{-17}\approx0.0452\times 10^{-17}=4.52\times 10^{-19}\ J$

Answer:

1. A. $6.63\times 10^{-34}\ Js$
2. B. $3.00\times 10^{8}\ m/s$
3. F. $4.52\times 10^{-19}\ J$
4. D. $440\times 10^{-9}\ m$