Question

The de Broglie wavelength of a sand grain weighing 2 mg blown by a wind of 10 m/s is:

A. 3.31×10⁻²⁹ m
B. 1.12×10⁻²⁹ m
C. 2.21×10⁻²⁹ m
D. 4.42×10⁻²⁹ m

Answer 1

To calculate the de Broglie wavelength of the sand grain, we use the equation λ = h / p, where λ is the wavelength, h is Planck's constant, and p is the momentum. Given the mass of the sand grain and the velocity of the wind, we can find the momentum and then substitute it into the equation to calculate the de Broglie wavelength.

The correct answer is A. 3.31×10⁻²⁹ m.

Step-by-step explanation:

To calculate the de Broglie wavelength of the sand grain, we can use the equation:

λ = h / p

where λ is the wavelength, h is Planck's constant (6.63 × 10¯³⁴ J·s), and p is the momentum of the particle.

We can find the momentum using the equation:

p = mv

where m is the mass of the sand grain and v is the velocity of the wind.

Given that the mass of the sand grain is 2 mg (2 × 10¯³ g) and the velocity of the wind is 10 m/s, we have:

p = (2 × 10¯³ g) × (10 m/s) = 2 × 10¯² g·m/s

To convert the momentum to SI units, we can use the conversion factor:

1 g·m/s = 10¯³ kg·m/s

Thus, the momentum is:

p = (2 × 10¯² g·m/s) × (10¯³ kg·m/s) = 2 × 10¯⁵ kg·m/s

Now, we can plug the values of h and p into the equation for the de Broglie wavelength:

λ = (6.63 × 10¯³⁴ J·s) / (2 × 10¯⁵ kg·m/s)

Calculating this equation gives the de Broglie wavelength as approximately 3.31 × 10¯²⁹ m.

Therefore, the correct answer is A. 3.31×10⁻²⁹ m.