Question

What is the de Broglie wavelength (in m) of a 1.8 g object moving at a speed of 2.8 m/s? a. 2.4x 10^34 m b. 2.4 x 10^37 m c. 1.3 x 10^51m d. 1.3 x 10^54 m e. 11x10^8 m

Answer 1

The de Broglie wavelength of a 1.8 g object moving at a speed of 2.8 m/s is approximately 1.316 × 10⁻³¹ m.

Step-by-step explanation:

The de Broglie wavelength of an object can be calculated using the formula:

λ = h / p

Where λ is the de Broglie wavelength, h is Planck's constant (which is approximately 6.63 × 10-34 Js), and p is the momentum of the object.

First, we need to calculate the momentum of the object. Momentum can be calculated using the formula:

p = mv

Where p is the momentum, m is the mass of the object, and v is the velocity of the object.

Given that the mass of the object is 1.8 g (which is equivalent to 0.0018 kg) and the velocity is 2.8 m/s, we can calculate the momentum:

p = (0.0018 kg)(2.8 m/s) = 0.00504 kg·m/s

Now, we can calculate the de Broglie wavelength:

λ = (6.63 × 10-34 Js) / (0.00504 kg·m/s) = 1.316 × 10-31 m

Therefore, the de Broglie wavelength of the 1.8 g object moving at a speed of 2.8 m/s is approximately 1.316 × 10-31 m.

Answer 2

The de Broglie wavelength of a 1.8 g object moving at 2.8 m/s is calculated using the formula λ = h / (mass × velocity), resulting in a wavelength of 1.3 × 10-34 m, which does not match any of the provided options.

Step-by-step explanation:

The subject of this question is physics, and specifically it pertains to quantum mechanics and the concept of de Broglie wavelengths as applied to macroscopic objects. According to de Broglie's hypothesis, every object has a wavelength associated with it, which can be calculated using the formula λ = h / p, where λ is the de Broglie wavelength, h is Planck's constant (6.62607015 × 10-34 m2 kg / s), and p is the momentum of the object (mass × velocity).

For an object with a mass of 1.8 g (which is 1.8 × 10-3 kg) moving at a speed of 2.8 m/s, its de Broglie wavelength λ can be calculated as:

λ = h / (mass × velocity) = 6.62607015 × 10-34 m2 kg / s / (1.8 × 10-3 kg × 2.8 m/s) = 1.3 × 10-34 m

Therefore, the correct answer is none of the options given, as the correct value would be of the order of 10-34 meters.