For the reaction P $$\to$$ B, the values of frequency factor A and activation energy E_A are 4 $$\times$$ 10¹³ s^$$-$$1 and 8.3 kJ mol^$$-$$1 respectively. If the reaction is of first order, the temperature at which the rate constant is 2 $$\times$$ 10^$$-$$6 s^$$-$$1 is _____________ $$\times$$ 10^$$-$$1 K.

(Given : ln 10 = 2.3, R = 8.3 J K^$$-$$1 mol^$$-$$1, log2 = 0.30)

The equation

k = (6.5 $$\times$$ 10¹²s^$$-$$1)e^{$$-$$26000K/T}

is followed for the decomposition of compound A. The activation energy for the reaction is ________ kJ mol^$$-$$1. [nearest integer]

(Given : R = 8.314 J K^$$-$$1 mol^$$-$$1)

The activation energy of one of the reactions in a biochemical process is 532611 J mol^$$-$$1. When the temperature falls from 310 K to 300 K, the change in rate constant observed is k₃₀₀ = x $$\times$$ 10^$$-$$3 k₃₁₀. The value of x is ____________.

[Given : $$\ln 10 = 2.3$$, R = 8.3 J K^$$-$$1 mol^$$-$$1]

A radioactive element has a half life of 200 days. The percentage of original activity remaining after 83 days is ___________. (Nearest integer)

(Given : antilog 0.125 = 1.333, antilog 0.693 = 4.93)