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balandron [24]
3 years ago
5

The half-life for radioactive decay (a first-order process) is 24,000 years. How many years does it take for one mole of this ra

dioactive material to decay so that just one atom remains?
Physics
1 answer:
iren [92.7K]3 years ago
4 0

Answer: it will take 1.9 × 10⁶ yrs for one mole of the radioactive material to decay so that just one atom remains

Explanation:

Given that;

Half life t_1/2 = 24,000 years

initial amount of radio active element = 1 mole

now one mole of a substance has Avagadro number of atoms which is initially 6.023 × 10²³ which are present and finally only 1 atom is left

using the formula

t_1/2 = 0.693/k

In[ N₀/N_t] = kt

N₀ is the initial amount, N_t is the amount left after t time, t is the time, k is the rate constant.

now we substitute

t_1/2 = 0.693/k

k = 0.693/ t_1/2

k = 0.693 / 24,000 years

k = 0.000028875 yr⁻¹

so

In[ N₀/N_t] = kt

t = 1/0.000028875 yr⁻¹ In [ 6.023 × 10²³ / 1 ]

= 34632.0346 In[6.023 × 10²³]

= 34632.0346 × 54.7550

= 1896277.0545 yrs ≈ 1.9 × 10⁶ yrs

Therefore it will take 1.9 × 10⁶ yrs for one mole of the radioactive material to decay so that just one atom remains

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Gelneren [198K]
Hmm...
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disadvantages: takes a large crew to maintain, mostly needs to be in an open area.
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disadvantages: unsightly, needs open space and costs a lot to build
Take your pick!

8 0
4 years ago
Read 2 more answers
Water at 20°C flows by gravity through a smooth pipe from one reservoir to a lower one. The elevation difference is 60 m. The pi
Serga [27]

Answer:

Flow Rate = 80 m^3 /hours  (Rounded to the nearest whole number)

Explanation:

Given

  • Hf = head loss
  • f = friction factor
  • L = Length of the pipe = 360 m
  • V = Flow velocity, m/s
  • D = Pipe diameter = 0.12 m
  • g = Gravitational acceleration, m/s^2
  • Re = Reynolds's Number
  • rho = Density =998 kg/m^3
  • μ = Viscosity = 0.001 kg/m-s
  • Z = Elevation Difference = 60 m

Calculations

Moody friction loss in the pipe = Hf = (f*L*V^2)/(2*D*g)

The energy equation for this system will be,

Hp = Z + Hf

The other three equations to solve the above equations are:

Re = (rho*V*D)/ μ

Flow Rate, Q = V*(pi/4)*D^2

Power = 15000 W = rho*g*Q*Hp

1/f^0.5 = 2*log ((Re*f^0.5)/2.51)

We can iterate the 5 equations to find f and solve them to find the values of:

Re = 235000

f = 0.015

V = 1.97 m/s

And use them to find the flow rate,

Q = V*(pi/4)*D^2

Q = (1.97)*(pi/4)*(0.12)^2 = 0.022 m^3/s = 80 m^3 /hours

7 0
3 years ago
A car is idling at a stoplight. When the light turns green, the car takes 12 seconds to accelerate to 18.7 m/s. What is the aver
Sonbull [250]

Answer:

1.6 m/s^2

Explanation:

3 0
4 years ago
A skateboarder is moving at 1.75 m/s when she starts going up an incline that causes an acceleration of -0.20 m/s2
Rudiy27

Answer:

Approximately 7.66\; \rm m.

Explanation:

<h3>Solve this question with a speed-time plot</h3>

The skateboarder started with an initial speed of u = 1.75\; \rm m \cdot s^{-1} and came to a stop when her speed became v = 0\; \rm m \cdot s^{-1}. How much time would that take if her acceleration is a = -0.20\; \rm m \cdot s^{-1}?

\begin{aligned} t &= \frac{v - u}{a} \\ &= \frac{0\; \rm m \cdot s^{-1} - 1.75\; \rm m \cdot s^{-1}}{-0.20\; \rm m \cdot s^{-2}} \approx 8.75\; \rm s\end{aligned}.

Refer to the speed-time graph in the diagram attached. This diagram shows the velocity-time plot of this skateboarder between the time she reached the incline and the time when she came to a stop. This plot, along with the vertical speed axis and the horizontal time axis, form a triangle. The area of this triangle should be equal to the distance that the skateboarder travelled while she was moving up this incline until she came to a stop. For this particular question, that area is approximately equal to:

\displaystyle \frac{1}{2} \times 1.75\; \rm m \cdot s^{-1} \times 8.75\; \rm s \approx 7.66\; \rm m.

In other words, the skateboarder travelled 15.3\; \rm m up the slope until she came to a stop.

<h3>Solve this question with an SUVAT equation</h3>

A more general equation for this kind of motion is:

\displaystyle x = \frac{1}{2}\, (u + v) \, t = \frac{1}{2}\, (u + v)\cdot \frac{v - u}{a}= \frac{v^2 - u^2}{2\, a},

where:

  • u and v are the initial and final velocity of the object,
  • a is the constant acceleration that changed the velocity of this object from u to v, and
  • x is the distance that this object travelled while its velocity changed from u to v.

For the skateboarder in this question:

\begin{aligned}x &= \frac{v^2 - u^2}{2\, a}\\ &= \frac{\left(0\; \rm m \cdot s^{-1}\right)^2 - \left(1.75\; \rm m \cdot s^{-1}\right)^2}{2\times \left(-0.20\; \rm m \cdot s^{-2}\right)}\approx 7.66\; \rm m \end{aligned}.

6 0
4 years ago
Explain how the theory of the Sun’s dynamo results in an average 22-year solar activity cycle. Include the location and mechanis
horrorfan [7]

Answer:

Explanation:

Sun's dynamo means the process that produce Sun's magnetic field.

The mechanism inside a Sun acts like a generator that produces electric current and magnetic field.

Magnetic field with in the Sun are extended out and around. Magnetic field of lines get twisted due to rotation of Sun.

The material that flows inside the Sun plays an important role in Sun's dynamo. At surface the flow rate is about 20 m/s but as it moves towards equator, it becomes way too slow taking about 11 years of time.

Due to the this magnetic field, several sun spots are formed on the surface.

The number of sunspots keep on changing from minimum to maximum number resulting into change in the magnetic pole. In each cycle polarity get reversed hence the overall magnetic cycle has an interval of 22 years.

5 0
3 years ago
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