It is desired to move a small, 50 kg cat in outer space by strapping a lamp, which emits 100 W of blue light to it. If the cat is free in space, and the wavelength of blue light is 470 nm, what would be the acceleration of the cat? (HINT: Consider how many photons are emitted by the lamp per second).

To calculate the acceleration of the cat, we need to consider the momentum transfer of the photons emitted by the lamp.

The momentum of a single photon is given by the formula:

p = h/λ

Where:
p is the momentum of the photon,
h is Planck's constant (6.626 x 10^-34 J*s), and
λ is the wavelength of the light.

In this case, we're given that the wavelength of blue light emitted by the lamp is 470 nm (or 470 x 10^-9 m). Therefore, we can calculate the momentum of a single photon using this wavelength.

p = (6.626 x 10^-34 J*s) / (470 x 10^-9 m)
p ≈ 1.41 x 10^-27 kg*m/s

Now, let's determine how many photons are emitted per second. To do that, we need to calculate the energy emitted per second by the lamp.

The power emitted by the lamp is given as 100 W (watts).

Power is defined as the energy emitted per unit time, so we can calculate the energy emitted per second using the formula:

Energy = Power x Time

In this case, the energy emitted per second is 100 J (joules).

Now, let's figure out the number of photons emitted per second. We can divide the total energy emitted per second (100 J) by the energy of a single photon (1.41 x 10^-27 J):

Number of photons per second = Energy emitted per second / Energy of a single photon

Number of photons per second = 100 J / (1.41 x 10^-27 J)
Number of photons per second ≈ 7.09 x 10^26 photons/s

Now that we know the number of photons emitted per second, let's calculate the total momentum transferred to the cat per second.

Total momentum transferred per second = Number of photons per second x Momentum of a single photon

Total momentum transferred per second = (7.09 x 10^26 photons/s) x (1.41 x 10^-27 kg*m/s)
Total momentum transferred per second ≈ 9.99 x 10^-2 kg*m/s

Since momentum is equal to mass multiplied by velocity, we can calculate the acceleration of the cat by dividing the total momentum transferred per second by the mass of the cat:

Acceleration = Total momentum transferred per second / Mass of the cat

Acceleration = (9.99 x 10^-2 kg*m/s) / 50 kg
Acceleration ≈ 1.998 x 10^-3 m/s^2

So, the acceleration of the cat in outer space, when subjected to the blue light emitted by the lamp, is approximately 1.998 x 10^-3 m/s^2.