Elements 36 and 54 have similar chemical properties. based on their electronic configurations, predict the atomic number of a heavier element that should also share these chemical properties. express your answer as an integer.

86  

Explanation:

The electron configuration of element 36 is

1s² 2s²2p⁶ 3s²3p⁶ 4s²3d¹⁰4p⁶

Now, we add 18 electrons to reach element 54. Its electron configuration is

1s² 2s²2p⁶ 3s²3p⁶ 4s²3d¹⁰4p⁶ 5s²4d¹⁰5p⁶

These elements have similar properties because their electron configurations end in p⁶.

To reach the next element with similar properties, we must add enough electrons to reach a p⁶ configuration.

We follow the Wiswesser diagram below to determine the sequence order of the subshells.

To reach a p⁶ configuration, we must add 32 electrons, because we must fill the 4f orbitals.

The electron configuration of the next element with similar properties is  

1s² 2s²2p⁶ 3s²3p⁶ 4s²3d¹⁰4p⁶ 5s²4d¹⁰5p⁶ 6s²5d¹⁰4f¹⁴6p⁶

And the element number is 54 + 32 = 86.  

part 1: the half-life of the element is 22 years.

part 2: it will take 132.02 year for the sample to decay from 308.0 g to 4.8125 g.

explanation:

part 1: there are two ways to determine the half life time.

first way: the half life time can be determined directly from its definition as it is the time required for the sample to decay to its half concentration.

from the data the initial concentration was 45.0 g and decayed to its half value (22.5 g) in 22.0 years.

second way: the radio active decay is considered first order reaction so we can use the laws of first order reactions.

k = (1/t) ln (a/a-x), where k is the rate constant of the reaction,

t is the time of the reaction

a is the initial concentration of the reactant

a-x is the remaining concentration at time (t)

a = 45.0 g the initial concentration at t = 0 year.

at t = 22 year, a-x = 22.5 g

then k = (1/22 year) ln (45.0 g/ 22.5 g) = 0.0315 year-1.

the half-life time (t1/2) = ln 2/ k = 0.693/ k =0.693/ 0.0315 = 22 years.

part 2:

using the same law k = (1/t) ln (a/a-x),

using the given data; a = 308.0 g and a-x = 4.8125 g and the calculated k from the part 1 (k = 0.0315 year-1)

t = (1/k) ln (a/a-x) = (1/0.0315) ln (308.0/ 4.8125) = 132.02 years

the earth would become to overheated and everything alive on it will eventually die from overheating. plants will eventually die as well, water will evaporate, and it will be nothing but a hot planet without anything living on it.