Answer:
144
Step-by-step explanation:
The answer is d, because you can make it into percent and make it into graphs
Answer : The time taken by the element to decay to 2 grams is, 75.2 minutes
Step-by-step explanation:
Half-life = 13 min
First we have to calculate the rate constant, we use the formula :
![k=\frac{0.693}{t_{1/2}}](https://tex.z-dn.net/?f=k%3D%5Cfrac%7B0.693%7D%7Bt_%7B1%2F2%7D%7D)
![k=\frac{0.693}{13\text{ min}}](https://tex.z-dn.net/?f=k%3D%5Cfrac%7B0.693%7D%7B13%5Ctext%7B%20min%7D%7D)
![k=0.0533\text{ min}^{-1}](https://tex.z-dn.net/?f=k%3D0.0533%5Ctext%7B%20min%7D%5E%7B-1%7D)
Now we have to calculate the time passed.
Expression for rate law for first order kinetics is given by:
![t=\frac{2.303}{k}\log\frac{a}{a-x}](https://tex.z-dn.net/?f=t%3D%5Cfrac%7B2.303%7D%7Bk%7D%5Clog%5Cfrac%7Ba%7D%7Ba-x%7D)
where,
k = rate constant = ![0.0533\text{ min}^{-1}](https://tex.z-dn.net/?f=0.0533%5Ctext%7B%20min%7D%5E%7B-1%7D)
t = time passed by the sample = ?
a = initial amount of the reactant = 110 g
a - x = amount left after decay process = 2 g
Now put all the given values in above equation, we get
![t=\frac{2.303}{0.0533}\log\frac{110}{2}](https://tex.z-dn.net/?f=t%3D%5Cfrac%7B2.303%7D%7B0.0533%7D%5Clog%5Cfrac%7B110%7D%7B2%7D)
![t=75.2\text{ min}](https://tex.z-dn.net/?f=t%3D75.2%5Ctext%7B%20min%7D)
Therefore, the time taken by the element to decay to 2 grams is, 75.2 minutes