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nordsb [41]
4 years ago
6

Every chemical element goes through natural exponential decay, which means that over time its atoms fall apart. The speed of eac

h element's decay is described by its half-life, which is the amount of time it takes for the number of radioactive atoms of this element to be reduced by half.
The half-life of the isotope beryllium-11 is 14 seconds. A sample of beryllium-11 was first measured to have 800 atoms. After t seconds, there were only 50 atoms of this isotope remaining, Write an equation in terms of t that models the situation.
Physics
2 answers:
laiz [17]4 years ago
7 0

Answer:

800 • (1/2)^t/14 = 50

Explanation:

Naddik [55]4 years ago
4 0

Answer:

t = (ti)ln(Ai/At)/ln(2)

t = 14ln(16)/ln(2)

Solving for t

t = 14×4 = 56 seconds

Explanation:

Let Ai represent the initial amount and At represent the final amount of beryllium-11 remaining after time t

At = Ai/2^n ..... 1

Where n is the number of half-life that have passed.

n = t/half-life

Half life = 14

n = t/14

At = Ai/2^(t/14)

From equation 1.

2^n = Ai/At

Taking the natural logarithm of both sides;

nln(2) = ln(Ai/At)

n = ln(Ai/At)/ln(2)

Since n = t/14

t/14 = ln(Ai/At)/ln(2)

t = 14ln(Ai/At)/ln(2)

Ai = 800

At = 50

t = 14ln(800/50)/ln(2)

t = 14ln(16)/ln(2)

Solving for t

t = 14×4 = 56 seconds

Let half life = ti

t = (ti)ln(Ai/At)/ln(2)

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SVETLANKA909090 [29]

Answer:11 km/s

Explanation:

Given

Escape velocity at the surface of earth is 11 km/s

Escape velocity is given by

V_e=\sqrt{\frac{2GM}{R}}

Escape velocity at the surface of earth

11=\sqrt{\frac{2GM}{R}}--------------------1

If Escape velocity is three times and the radius is also the three times

V_e_2=\sqrt{\frac{2G(3M)}{3R}}

V_e_2=\sqrt{\frac{2GM}{R}}=V_e

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5 0
3 years ago
The y-axis on a distance-time graph would be ____________. time distance speed
natita [175]

Answer:

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Explanation:

distance is in vertical axis,or y-axis and time is on the horizontal axis,or x-axis.

7 0
3 years ago
Acar moving at 25 m/s slams on its brakes and comes to rest in a time interval of 5 sec. Calculate the average acceleration of t
Artyom0805 [142]

Answer:

Explanation:

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since the car stoped do its final velocity or v2 is equal 0

8 0
3 years ago
Two manned satellites approaching one another at a relative speed of 0.450 m/s intend to dock. The first has a mass of 4.50 ✕ 10
vovangra [49]
Ok, so adopting that the 2nd satellite is at rest and that we're not moving anywhere near the speed of light (so no special relativity considerations), we can just add the two speed together, and say the 1st satellite is moving at 0.9m/s at the 2nd satellite. We can then set up our conservation of momentum equation, m₁v₁+m₂v₂ = m₁v₃+m₂v₄, where I'm calling v 1 and 2 the initial velocities of satellite 1 and 2 and v 3 and 4 the final velocities of satellite 1 and 2 respectively. We know, based on our chosen frame, that v₂ = 0, so that falls out to leave m₁v₁ = m₁v₃+m₂v₄, but we don't know v₃ or v₄, so we need another equation. Let's set up conversation of energy (elastic collisions conserve energy), where we only have to worry about kinetic energy (K = 1/2mv²) for each satellite before and after the collision. So we get 1/2m₁v₁²+1/2m₂v₂² = 1/2m₁v₃²+1/2m₂v₄². Now we have 2 equations and two unknown variables so let's solve with substitution. Let's solve the momentum equation for v₃, v₃ = (m₁v₁ - m₂v₄)/m₁, sub that into the energy equation, cancel the 1/2's and let's drop the v₂ terms since it's zero and we get: m₁v₁² = m₁((m₁v₁ - m₂v₄)/m₁)²+m₂v₄², then after some algebra we get v₄ = sqrt(m₁v₁/((v₁ - m₂/m₁)²+m₂)), then we plug in numbers v₄ = sqrt((4.5*10³*0.9/((0.9-(7.5/4.5))²+7.5*10³) = 0.73 m/s for the 2nd satellite after the collision. Then go back to v₃ = (m₁v₁ - m₂v₄)/m₁ and plug in numbers now that we know v₄ and we get v₃ = (4.5*10³*0.9 - 7.5*10³*0.73)/(4.5*10³) = -0.3167 m/s for the 1st satellite.
6 0
3 years ago
If given both the speed of light in a material and an incident angle. How can you find the refracted angle?
Basile [38]

Answer:

r = Sin^{-1}\left ( \frac{v Sini}{c} \right )

Explanation:

Let the speed of light in vacuum is c and the speed of light in medium is v. Let the angle of incidence is i.

By using the definition of refractive index

refractive index of the medium is given by

n = speed of light in vacuum / speed of light in medium

n = c / v  ..... (1)

Use Snell's law

n = Sin i / Sin r

Where, r be the angle of refraction

From equation (1)

c / v = Sin i / Sin r

Sin r = v Sin i / c

r = Sin^{-1}\left ( \frac{v Sini}{c} \right )

8 0
4 years ago
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