Question

what is the wavelength of a 46 g golf ball travelling at 70 m/s?

o 4.86 x 10^33 m
o 2.06 x 10^-34 m
o 547 nm
o 0.782 nm
o 2.06 x 10^-37 m

Explanation:

Step1: Convert mass to SI unit

The mass of the golf - ball $m = 46\ g=0.046\ kg$. The velocity $v = 70\ m/s$. We use the de - Broglie wavelength formula $\lambda=\frac{h}{p}$, where $h = 6.63\times10^{-34}\ J\cdot s$ is Planck's constant and $p = mv$ is the momentum.

Step2: Calculate the momentum

$p=mv=(0.046\ kg)\times(70\ m/s)=3.22\ kg\cdot m/s$.

Step3: Calculate the wavelength

$\lambda=\frac{h}{p}=\frac{6.63\times 10^{-34}\ J\cdot s}{3.22\ kg\cdot m/s}\approx2.06\times 10^{-34}\ m$.

Answer:

$2.06\times 10^{-34}\ m$ (Second option)