Answer:
10,000 years
Explanation:
Given that,
Half life of the radioactive isotope,
= 5000 years
Initial composition,
= 16 grams
Final composition,
= 4 grams
We know that,

Therefore, the age of the rock is 10,000 years.
It will spread faster in the hot water! It would spread slower in cold water
Answer: 8.1 x 10^24
Explanation:
I(t) = (0.6 A) e^(-t/6 hr)
I'll leave out units for neatness: I(t) = 0.6e^(-t/6)
If t is in seconds then since 1hr = 3600s: I(t) = 0.6e^(-t/(6 x 3600) ).
For neatness let k = 1/(6x3600) = 4.63x10^-5, then:
I(t) = 0.6e^(-kt)
Providing t is in seconds, total charge Q in coulombs is
Q= ∫ I(t).dt evaluated from t=0 to t=∞.
Q = ∫(0.6e^(-kt)
= (0.6/-k)e^(-kt) evaluated from t=0 to t=∞.
= -(0.6/k)[e^-∞ - e^-0]
= -0.6/k[0 - 1]
= 0.6/k
= 0.6/(4.63x10^-5)
= 12958 C
Since the magnitude of the charge on an electron = 1.6x10⁻¹⁹ C, the number of electrons is 12958/(1.6x10^-19) = 8.1x10^24 to two significant figures.
Explanation:
Resistors connected in series obey the following equation:

Resistors connected in parallel obey the following equation:

The total current of the circuit will obey the Ohm's Law: V = IR. And the current will be divided across the resistors (bulbs) depending on their resistances. So, if a bulb has a higher resistance, then its current will be lesser, and it will be less bright. If a bulb has a lower resistance, then its current will be higher, and it will be brighter.
According to the above resistances connected in series and parallel, clearly, the resistances (bulbs) connected in series will have more resistance in total, and therefore less current will flow across them, and they will be less bright.