All categories

3 years ago

What is the half-life of a radioisotope

2 answers:

4 0

The rate at which a radioactive isotope decays is measured in half-life. The termhalf-life is defined as the time it takes for one-half of the atoms of a radioactive material to disintegrate. Half-lives for various radioisotopes can range from a few microseconds to billions of years.

HACTEHA [7]3 years ago

4 0

Answer:

It is the time after which a given sample of radioactive substance will decay to half of the initial number present in the sample.

Explanation:

As we know that as per law of radioactivity the number of radioactive nuclei present in the sample is proportional to the rate of decay

so it is given by

$\frac{dN}{dt} = -\lambda N$

after solving above relation we will have

$N = N_0e^{-\lambda t}$

now here we know that as the number of nuclei is reduced to half of the initial number then we have

$\frac{N_0}{2} = N_0e^{-\lambda t}$

$t = \frac{ln2}{\lambda}$

so this time is known as half life where the denominator of the equation is known as decay constant.

You might be interested in

When you turn up the volume on a radio, which of the following change: velocity of sound, intensity, pitch, amplitude, frequency

Xelga [282]

Loudness
its
true
trust in the hope

5 0

3 years ago

Read 2 more answers

Can you walk on the moon

morpeh [17]

You can. But the gravity on the moon is 1/6th the gravity on Earth. This means 300 lbs man would only weigh 50 lbs.

7 0

3 years ago

Read 2 more answers

A 100 kg box is suspended from two ropes. The "left rope makes an angle of 20" degrees with the vertical, and the right rope mak

GarryVolchara [31]

Explanation:

It is given that,

Mass of the box, m = 100 kg

Left rope makes an angle of 20 degrees with the vertical, and the right rope makes an angle of 40 degrees.

From the attached figure, the x and y component of forces is given by :

$T_{1x} =-T_1 cos (20)$

$T_{2x} = T_2 cos (40)$

$mg_x = 0$

$T_{1y} = T_1 sin (20)$

$T_{2y} = T_2 sin (40)$

$mg_y= -mg$

Let $R_x$ and $R_y$ is the resultant in x and y direction.

$R_x=-T_1 cos (20)+T_2 cos (40)+0$

$R_y=T_1 sin(20)+T_2 sin(40)-mg$

As the system is balanced the net force acting on it is 0. So,

$-T_1 cos (20)+T_2 cos (40)+0=0$ .............(1)

$T_1 sin(20)+T_2 sin(40)-100\times 9.8=0$ ..................(2)

On solving equation (1) and (2) we get:

$T_1=866.86\ N$ (tension on the left rope)

$T_2=1063.36\ N$ (tension on the right rope)

So, the tension on the right rope is 1063.36 N. Hence, this is the required solution.

7 0

3 years ago

Jake is helping Fin push a box at a constant velocity up an incline that makes an angle of 30.0° above the horizontal by applyin

andre [41]

Given data

The angle of inclination of the plane is theta = 30 degree

The applied force in the inclined plane is F = 94 N

The distance moved in the inclined plane is d = 2.30 m

The coefficient of kinetic friction is u_k = 0.280

The free-body diagram of the above configuration is shown below:

Here, the normal reaction force on the box is N, the acceleration due to gravity is denoted as g, the friction force on the box is F_f, and the mass of the box is denoted as m.

(a)

The expression for the work done by the pushing force is given as:

$W=Fd$

Substitute the value in the above equation.

$\begin{gathered} W=94\text{ N}\times2.30\text{ m} \\ W=216.2\text{ J} \end{gathered}$

Thus, the work done by the pushing force is 216.2 J.

(b)

The box is moving at the constant velocity, therefore, the pushing force will be equal to the frictional force and the component of the gravitational force in the inclined plane.

$\begin{gathered} F=F_f+mg\sin \theta \\ F=\mu_kN+mg\sin \theta \end{gathered}$

The expression for the normal reaction force is given as:

$N=mg\cos \theta$

The expression for the mass of the box is given as:

$\begin{gathered} F=\mu_k\times mg\cos \theta+mg\sin \theta \\ m=\frac{F}{\mu_kg\cos \theta+g\sin \theta} \end{gathered}$

Substitute the value in the above equation.

$\begin{gathered} m=\frac{94\text{ N}}{0.28\times9.8m/s^2\times\cos 30^o+9.8m/s^2\times\sin 30^0} \\ m=12.9\text{ kg} \end{gathered}$

Thus, the mass of the box is 12.9 kg.

7 0

1 year ago

Scientists _____. Select all that apply.

Annette [7]

The true answer is the choice A
Scientists can predict volcanic eruptions as long as adequate resources are available.Volcanic eruptions are one of the earthly activities which can be predicted by means of adequate resources (warming of the earth's crust, appearance of volcanic lava etc...). By contrast, earthquakes is a dangerous natural disaster that scientists cannot be predicted or mastering the time where it occurs.

5 0

4 years ago