Question

Calculate the wavelength, in meters, associated with a 1.0 x 10^2 g golf ball moving at 27 m/s (about 60. mph).

Wavelength = m

Consider a 1.0 x 10^2 g golf ball. At what speed must the ball travel to have a wavelength of 5.6 x 10^-3 nm?
Speed= m x s^-1

Answer 1

Answer:

Question 1: ${\lambda = 2.45*10^{-34}m.$

Question 2: $v=8.45*10^{20}m/s$.

Explanation:

The de broglie wavelength is given by

$\lambda = \dfrac{h}{mv}$

where $m$ is the mass of the ball, $v$ is its velocity, and $h =6.63*10^{-34}J\cdot s$ is the plank's constant.

Now, in the case of the golf ball

$m= 1.0*10^2*10^{-3}kg$

$v =27m/s$;

therefore, the de broglie wavelength is

$\lambda = \dfrac{6.63*10^{-34}}{(1.0*10^{-1}kg)(27m/s)}$

$\boxed{\lambda = 2.45*10^{-34}m.}$

For the second question

$\lambda = 5.6*10^{-3}*10^{-9}m$,

therefore the de broglie relation gives

$5.6*10^{-3}*10^{-9}=\dfrac{6.63*10^{-34}}{1.0*10^{-1}v}$

solving for $v$ we get:

$v=8.45*10^{20}m/s$

which is way larger than the speed of light, and therefore, the golf ball can never have this wavelength!

Answer 2

The wavelength of the golf ball moving at 27 m/s is 2.456 * 10⁻³⁷ m

De Broglie formula

De Broglie formula is given by:

Wavelength (λ) = Planks constant (h) / (mass (m) * velocity (v))

a) Given that:

v = 27 m/s, h = 6.63 * 10⁻³⁴ J.s, m = 1 * 10² kg, hence:

λ = 6.63 * 10⁻³⁴ / (27 * 1 * 10²) = 2.456 * 10⁻³⁷ m

b) Given that:

λ = 5.6 * 10⁻³ nm =  5.6 * 10⁻¹² m, h = 6.63 * 10⁻³⁴ J.s, m = 1 * 10² kg, hence:

5.6 * 10⁻¹² m = 6.63 * 10⁻³⁴ / (v * 1 * 10²)

v = 1.18 * 10⁻²⁴ m/s

The wavelength of the golf ball moving at 27 m/s is 2.456 * 10⁻³⁷ m

Find out more on de Broglie at: https://brainly.com/question/5440536