The size and cultural characteristics of a group of people ultimately depends upon the soil and climate of the area. True False

For a proton in the ground state of a 1-dimensional infinite square well, what is the probability of finding the proton in the c

Butoxors [25]

Answer:

The probability of finding the proton at the central 2% of the well is almost exactly 4%

Explanation:

If we solve Schrödinger's equation for the infinite square well, we find that its eigenfunctions are sinusoidal functions, in particular, the ground state is a sinusoidal function for which only half a cycle fits inside the well.

let $L$ be the well's length, the boundary conditions for the wavefunction are:

$\psi(0) = \psi(L) =0$

And Schrödinger's equation is:

$- \frac{\hbar^2}{2m} \frac{d^2\psi}{dx^2} = E\psi$

The solution to this equation are sines and cosines, but the boundary conditions only allow for sine waves. As we pointed out, the ground state is the sine wave with the largest wavelength possible (that is, with the smallest energy).

$\psi_0(x)=\sqrt[]{\frac{2}{L} }\, \sin(\frac{\pi x}{L} )\\$

here the leading constant is just there to normalise the wavefunction.

Now, if we know the wavefunction, we can know what the probability density function is, it is:

$f_X(x) = |\psi|^2$

So in our case:

$f_X(x) = \frac{2}{L} \sin^2(\frac{\pi x}{L})$

And to find the probability of finding the particle in a strip at the centre of the well of width 2% of L we only have to integrate:

$P(X \in [0.49 L, 0.51L ])= \int\limits^{0.49L}_{0.51L } {\frac{2}{L} \sin^2(\frac{\pi x}{L})} \, dx$

If we do a substitution:

$x = u \, L$

We get the integral:

$\int\limits^{0.49}_{0.51 } 2\, \sin^2(\pi u)} \, du$

This integral can be computed analytically, and it's numerical value is .0399868, that is, almost a 4% probability.

5 0

3 years ago

Two fans are watching a baseball game from different positions. One fan is located directly behind home plate, 18.3 mfrom the ba

hjlf

Answer:

Δt = 0.315s

Explanation:

To calculate the time difference, in which both fans hear the batterstrike, you first calculate the time which takes the sound to travel the distances to both fans:

$t_1=\frac{d_1}{v_s}$

$t_2=\frac{d_2}{v_s}$

d1: distance to the first fan = 18.3 m

d2: distance to the second fan = 127 m

vs: speed of sound = 345 m/s

You replace the values of the parameters to calculate t1 and t2:

$t_1=\frac{18.3m}{345m/s}=0.053s\\\\t_2=\frac{127m}{345m/s}=0.368s$

The difference in time will be:

$\Delta t =t_2-t_2=0.368s-0.053s=0.315s$

Hence, the time difference between hearing the sound at the location s of both fans is 0.315s

4 0

3 years ago

If you had a known sample of a mineral whose density was 7.1 grams/ml and its volume was 15 ml. What is the mass of the mineral.

kow [346]

Answer:

<h3>The answer is 106.5 g</h3>

Explanation:

The mass of a substance when given the density and volume can be found by using the formula

<h3>mass = Density × volume</h3>

From the question

volume = 15 mL

density = 7.1 g/mL

We have

mass = 7.1 × 15

We have the final answer as

Hope this helps you

6 0

3 years ago

during a crash a dummy with the mass of 60.0 kg hits a airbag that exerts a constant force in the dummy the acceleration of the

Yakvenalex [24]

Explanation:

F = ma

F = (60.0 kg) (250 m/s²)

F = 15,000 N

6 0

3 years ago

What process marks the birth of a star?

Misha Larkins [42]

Answer:

Magic school bus on ya left! so basically a star is born when like....atoms are like squeezed with enough pressure and kinda squished together, once tht happens the atoms start to fuse together

Explanation:

7 0

4 years ago