How to solve the question

A system contains n atoms, each of which can only have zero or one quanta of energy. How many ways can you arrange r quanta of e

My name is Ann [436]

Answer:

$\mathbf{a)} 2\\ \\ \mathbf{b)} 184 \; 756 \\ \\\mathbf{c)} \dfrac{(2\times 10^{23})!}{(10^{23}!)(10^{23})!}$

Step-by-step explanation:

If the system contains $n$ atoms, we can arrange $r$ quanta of energy in

$\binom{n}{r} = \dfrac{n!}{r!(n-r)!}$

ways.

$\mathbf{a)}$

In this case,

$n = 2, r=1$ .

Therefore,

$\binom{n}{r} = \binom{2}{1} = \dfrac{2!}{1!(2-1)!} = \frac{2 \cdot 1}{1 \cdot 1} = 2$

which means that we can arrange 1 quanta of energy in 2 ways.

$\mathbf{b)}$

In this case,

$n = 20, r=10$ .

Therefore,

$\binom{n}{r} = \binom{20}{10} = \dfrac{20!}{10!(20-10)!} = \frac{10! \cdot 11 \cdot 12 \cdot \ldots \cdot 20}{10!10!} = \frac{11 \cdot 12 \cdot \ldots \cdot 20}{10 \cdot 9 \cdot \ldots \cdot 1} = 184 \; 756$

which means that we can arrange 10 quanta of energy in 184 756 ways.

$\mathbf{c)}$

In this case,

$n = 2 \times 10^{23}, r = 10^{23}$ .

Therefore, we obtain that the number of ways is

$\binom{n}{r} = \binom{2\times 10^{23}}{10^{23}} = \dfrac{(2\times 10^{23})!}{(10^{23})!(2\times 10^{23} - 10^{23})!} = \dfrac{(2\times 10^{23})!}{(10^{23}!)(10^{23})!}$

3 0

3 years ago

Please help with geometry! Will give thanks and brainliest answer.

lorasvet [3.4K]

B - 63 Degrees, obviously because all angles add up to a sum of 180 degrees.

6 0

3 years ago

Brooke found the equation of the line passing through the points (–7, 25) and (–4, 13) in slope-intercept form as follows. Step

Katen [24]

Answer: She mixed up the slope and y-intercept when she wrote the equation in step 3.

Step-by- explanation:

Hope this helps :)

8 0

3 years ago

Read 2 more answers

on monday, a parking garage was 60% full, with 120 cars parked. on tuesday, there were 30 more cars parked jn the garage than th

vlada-n [284]

Answer:

75%

Step-by-step explanation:

we know that 60% of x is 120. we can rewrite this to .6x = 120, to get x we divide both sides by .6, so x = 200. now 120 + 30 = 150. then we divide 150 out of 200 which is .75 it 75%

8 0

3 years ago

A solid cylinder of iron whose diameter is 18 cm and height 12 cm is melted and turned into a solid sphere. Find the diameter of

finlep [7]

Answer:

Diameter of sphere = 18 cm

Step-by-step explanation:

<h2>Volume of Cylinder and Sphere:</h2><h3> Cylinder:</h3>

Diameter = 18 cm

r = 18÷ 2 = 9 cm

h = 12 cm

$\sf \boxed{\bf Volume \ of \ cylinder = \pi r^2h}$

= π * 9 * 9 * 12 cm³

<h3>Sphere:</h3>

$\sf \boxed{\text{\bf Volume of sphere = $\dfrac{4}{3} \pi r^3$}}$

Solid cylinder is melted and turned into a solid sphere.

Volume of sphere = volume of cylinder

$\sf \dfrac{4}{3}\pi r^3 = \pi *9*9*12$

$\sf r^{3}= \dfrac{\pi *9*9*12*3}{4*\pi }\\\\ r^{3}=9 * 9 *3 *3\\\\\\r = \sqrt[3]{9*9*9}\\\\ r = 9 \ cm\\\\diameter = 9*2\\\\\boxed{diameter \ of \ sphere = 18 \ cm}$

6 0

2 years ago