Consider a quantum system which has only two linearly independent states denoted by vectors i0) and 1). the hilbert space of such system is 2-dimensional. let vectors 10) and |1) be the basis vectors. furthermore, leta=(a b)be the hamiltonian of the system, with a and b being some real constants (a) write vectors 10) and |1) as column vectors. (b) find the normalized eigenvectors and the corresponding eigenstates of the hamiltonian. (c) this hamiltonian leads to time-dependence of the system state. assuming that at t0, the system state vector is [0), what is the state vector at later times?

28. evolution

29. environment, survive, offspring  

explanation:

answer: the correct answer is 1.

explanation: there are various process in which a radioactive nuclei decays:

1) alpha decay: in this process, a heavier nuclei decays into lighter nuclei by releasing alpha particle. the mass number is reduced by 4 units.

2) electron capture: in this decay process, a parent nuclei absorbs an electron and gets converted into a neutron. simply, a proton and an electron combines together to form a neutron. mass number does not change in this process.

3) gamma ray emission: it is a decay process in which an unstable nuclei gives excess energy by a spontaneous electromagnetic process. this decay releases . this process does not change the mass number.

4) positron emission: it is a type of decay process, in which a proton gets converted to neutron and an electron neutrino. this is also known as -decay. in this the mass number remains same.

from the above information, we see that only alpha-decay is producing a change in the mass number of the nucleus.

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b.

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