Radioactivity: Activity, gamma radiation and time required

Please answer the following questions (attached) with full explanations thankyou.

Isotope

A radioactive isotope has a decay constant lambda = 0.0582 s-1. a) What is the half-life of the isotope in seconds? b) What fraction of the activity of a sample of the isotope will remain after 30 seconds? c) Identify the name of the isotope.

Nuclear Physics

A patient undergoing radiation therapy for cancer receives a 215-rad dose of radiation. (a) Assuming that the cancerous growth has a mass of 0.17kg, calculate how much energy it absorbs. (b) Assuming the growth to have the specific heat of water, determine its increase in temperature. Answer A. 0.37 J B 0.51 mK A drug prepared for a patient is tagged with 99 Tc, which has a half-life of 6.05h. 43 (a) What is the decay constant of this isotope? (B) How many nuclei are required to give an activity of 1.50 uCi? Answer A. 0.115h^-1 B. 1.7x10^9 nuclei

Radioactivity

A radioactive source in the form of a metallic sphere of radius 10^-2 m emits beta particles at the rate of 10^10 particles per second. The source is electrically insulated. What is the time required for its potential to be raised by 4 V assuming 50% of the emitted beta particles escape the source ?

Forces

(See attached file for full problem description)