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3 years ago

How do you find the mass number of an isotope?

Chemistry

1 answer:

solong [7]3 years ago

8 0

Answer:

The mass number of an isotope is the total number of protons and neutrons in an atomic nucleus. If you know that a nucleus has 6 protons and 6 neutrons, then its mass number is 12. If the nucleus has 6 protons and 7 neutrons, then its mass number is 13.

Explanation:

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A certain radioactive isotope decays at a rate of 0.2% annually. Determine the half-life of this isotope, to the nearest year

pychu [463]

Answer:

The half-life of the radioactive isotope is 346 years.

Explanation:

The decay rate of the isotope is modelled after the following first-order linear ordinary differential equation:

$\frac{dm}{dt} = -\frac{m}{\tau}$

Where:

$m$ - Current isotope mass, measured in kilograms.

$t$ - Time, measured in years.

$\tau$ - Time constant, measured in years.

The solution of this differential equation is:

$m(t) = m_{o}\cdot e^{-\frac{t}{\tau} }$

Where $m_{o}$ is the initial mass of the isotope. It is known that radioactive isotope decays at a yearly rate of 0.2 % annually, then, the following relationship is obtained:

$\%e = \frac{m(t)-m(t+1)}{m(t)}\times 100\,\% = 0.2\,\%$

$1 - \frac{m(t+1)}{m(t)} = 0.002$

$1 - \frac{m_{o}\cdot e^{-\frac{t+1}{\tau} }}{m_{o}\cdot e^{-\frac{t}{\tau} }}=0.002$

$1 - e^{-\frac{1}{\tau} } = 0.002$

$e^{-\frac{1}{\tau} } = 0.998$

$-\frac{1}{\tau} = \ln 0.998$

The time constant associated to the decay is:

$\tau = -\frac{1}{\ln 0.998}$

$\tau \approx 499.500\,years$

Finally, the half-life of the isotope as a function of time constant is given by the expression described below:

$t_{1/2} = \tau \cdot \ln 2$

If $\tau \approx 499.500\,years$ , the half-life of the isotope is:

$t_{1/2} = (499.500\,years)\cdot \ln 2$

$t_{1/2}\approx 346.227\,years$

The half-life of the radioactive isotope is 346 years.

6 0

3 years ago

Fill in the missing data point. Show all calculations leading to an answer.

Aleksandr-060686 [28]

Answer:

1090 mmHg

Explanation:

We know that with gases we must use a Kelvin temperatures, so let’s try a plot of pressure against the Kelvin temperature.

We can create a table as follows

t/°C T/K p/mmHg

10 283 726

20 293 750

40 313 800

70 343 880

100 373 960

150 423 ???

I plotted the data and got the graph in the figure below.

It appears that pressure is a linear function of the Kelvin temperature.

y = mx + b

where x is the slope and b is the y-intercept.

===============

Calculate the slope

I will use the points (275, 700) and (380, 975).

Slope = Δy/Δx = (y₂ - y₁)/(x₂ -x₁) = (975 -700)/(380 – 275) = 275/105 = 2.619

So,

y = 2.619x + b

===============

Calculate the intercept

When x = 275, y = 700.

700 = 2.619 × 275 + b

700 = 720 + b Subtract 720 from each side and transpose.

b = -20

So, the equation of the graph is

y = 2.619x -20

===============

Calculate the pressure at 423 K (150°C)

y = 2.619 × 423 - 20

y = 1110 - 20

y = 1090

At 150 °C, the pressure 1090 mmHg.

The point is approximately at the position of the black dot in the graph.

7 0

3 years ago

HELP ME I WILL GIVE YOU 50 POINTS AND MAKE YOU BRAINIEST

hoa [83]

THEY ARE ALL NONMETALS ARE THE CORRECTA NSWER

5 0

3 years ago

Read 2 more answers

For the Bradford assay, the instructor will make a Bradford reagent dye by mixing 50 ml of 95% v/v ethanol with 100 mg of Coomas

Flauer [41]

Answer:

4.25% is the final concentration of phosphoric acid.

Explanation:

Initial concentration of phosphoric acid = $C_1=85\%=0.85$

Initial volume of phosphoric acid = $V_1=50 mL$

Final concentration of phosphoric acid = $C_2=?$

Final volume of phosphoric acid = $V_2=1 L=1000 mL$

( 1L = 1000 mL)

$C_1V_1=C_2V_2$

$C_2=\frac{C_1times V_1}{V_2}$

$=\frac{0.85\times 50 mL}{1000 mL}=0.0425=4.25%$

4.25% is the final concentration of phosphoric acid.

4 0

3 years ago

I need help for these I don’t really get them

Nataly_w [17]

It b and c I think I’m not sure

5 0

3 years ago