Which of these is an advantage of shade-grown coffee beans?

The initial activity of 37Ar is 8540 disintegrations per minute. After 10.0 days, the activity is 6990 disintegrations per minut

mylen [45]

Answer:

Approximately 3318 disintegrations per minute.

Explanation:

The activity $A$ of a radioactive decay at time $t$ can be found with the following equation:

$\displaystyle A(t) = A_0 \cdot \mathrm{e}^{-\lambda\cdot t}$ .

In this equation,

$\mathrm{e}$ is the natural base. $\mathrm{e}\approx 2.71828$ .
$A_0$ is the initial activity of the decay. For this question, $A_0 = \rm 8540\; min^{-1}$ .
The decay constant $\lambda$ of this sample needs to be found.

The decay constant here can be found using the activity after 10 days. As long as both times are in the same unit (days in this case,) conversion will not be necessary.

$A(10) = A_0\cdot \mathrm{e}^{\rm -\lambda \times 10\;day}= (\mathrm{8540\; min^{-1}})\cdot \mathrm{e}^{\rm -\lambda \times 10\;day}$ .

$A(10) = \rm 6690\; min^{-1}$ .

$\displaystyle \frac{\rm 6690\; min^{-1}}{\mathrm{8540\; min^{-1}}} = \mathrm{e}^{\rm -\lambda \times 10\;day}$

Apply the natural logarithm to both sides of this equation.

$\displaystyle \ln{\left(\frac{\rm 6690\; min^{-1}}{\mathrm{8540\; min^{-1}}}\right)} = \ln{\left(\mathrm{e}^{\rm -\lambda \times 10\;day}\right)}$ .

$\displaystyle \rm -\lambda \cdot (10\;day) = \ln{\left(\frac{\rm 6690\; min^{-1}}{\mathrm{8540\; min^{-1}}}\right)}$ .

$\displaystyle \rm \lambda= \rm \frac{\displaystyle \ln{\left(\frac{\rm 6690\; min^{-1}}{\mathrm{8540\; min^{-1}}}\right)}}{-10 \; day} \approx 0.0200280\; day^{-1}$ .

Note that the unit of the decay constant $\lambda$ is $\rm day^{-1}$ (the reciprocal of days.) The exponent $-\lambda \cdot t$ should be dimensionless. In other words, the unit of $t$ should also be days. This observation confirms that there's no need for unit conversion as long as the two times are in the same unit.

Apply the equation for decay activity at time $t$ to find the decay activity after 47.2 days.

$\displaystyle \begin{aligned}A(t)& = A_0 \cdot \mathrm{e}^{-\lambda\cdot t}\\&\approx \rm \left(8540\; min^{-1}\right)\cdot \mathrm{e}^{-0.0200280\; day^{-1}\times 47.2\;day}\\&\approx \rm 3318\; min^{-1}\end{aligned}$ .

By dimensional analysis, the unit of activity here should also be disintegrations per minute. The activity after 47.2 days will be approximately 3318 disintegrations per minute.

8 0

3 years ago

Why do scientists look for patterns in the world?

White raven [17]

So they can predict what happens next

4 0

2 years ago

Read 2 more answers

HELP PLEASEE

GarryVolchara [31]

Answer:

Let's start with the fact that cereals , are made of grains and are mostly carbohydrates. therefore they contain carbon oxygen and hydrogen. They also contain proteins so have nitrogen. Plants have the minerals that are in the soil where they grow, so the list you have is correct. They also generally have added vitamins ad minerals. The vitamins contain C, H, O N, and a few others such as sulfur, The added minerals might contain:copper, iron, zinc, cobalt, selenium, silicon and molybdenum .

Mark me as brainliest if it was helpful

4 0

2 years ago

How you could use a microscope to determine if a simple was either a prokaryote or a eukaryote

Black_prince [1.1K]

You could check if their cells had a nucleus or not. If it did it would be a eukaryote, if it did not then it would be a prokaryote.

3 0

3 years ago

Read 2 more answers

AN object has a volume<br> of 77ml and a mass of<br> 429. What is the density<br> of this object?

pantera1 [17]

Answer:

4.254320865115cm or simplied 4.25cm

Explanation:

6 0

2 years ago