In a binomial or a scientific name does genus name same for all members of a same family?
No a "family" is a higher order classification and includes (usually) many genera (it CAN contain only one).
Surely you can find on the internet the hierarchy of taxonomic terms?
Taxonomy is a method of cubbyholing living things into categories - an attempt by the human mind to apply some kind of template on how living things originated, are related, are identified.
Taxonomy attempts to put related things together showing their relative "closeness", species and family are part of the effort. As phinds said, one family can have one or many species assigned to it. A family name generally ends with "aceae".
This example answers your question directly:
Prunus persicus is the peach tree. It is in the family Rosaceae.
Rosa canina is the dog rose, a very pretty but stinky rose. It is also in the family Rosaceae.
So, the order from species -> family is:
species -> genus -> family. There can be just one genus or many genera in a family.
Sometimes a family has "too many" of genera in it - like the Nightshade family (potato, tomato, belladonna) called the Solanaceae. We created sub-families for the Solanaceae. These exist (just like the other divisions) for our convenience. They help a lot in identifying plants you have not seen before, for example.
One final point. Just because things look like they are very closely related does not mean they actually belong in the same branch of our taxonomy. My first taxonomy books had water lillies and the lotus plant in the same plant family.
A lot of their morphology (what they look like to your eye and under the microscope) is very, very similar. So the book said that the lotus closest living relative is water lily.
After DNA analysis of the two plants, it turns out that Lotus is off all by itself in its own family, the Nelumbonaceae. It closest relative is the plane tree (sycamore in the US). And it is not even much of a close relative.
so members having same genera would be in same family and members with same species would be in same genus right?
I think perhaps you are misunderstanding species. What exactly do you mean by "members with the same species"? If you mean two different things that have the same species, then yes they would have the same species.
For example, in wood, one of the more common rosewoods is Dalbergia latifolia. Dalbergia is the genus and latifolia is the specific epithet and when they are taken together they are called the "binomial name" or the "species". Strictly speaking, latifolia is NOT the species it's just the specific epithet. In any case, two different pieces of Dalbergia latifolia are both Dalbergia latifolia but that's just a tautology, which is why I don't quite understand your question.
you caught the correct point, i thought latifolia is species name because in definition of binomial name it was written that it consist of two words first genus name is written with first letter capital here Dalbergia and then species name with all small letters so in this case it should be latifolia what i am missing?and what is specific epithet ?
What you are quoting is common usage, even though not technically correct. "Species" is a term that identifies the lowest level of organism in taxonomy (to get REALLY technical there are occasional exceptions) and can only be expressed by the full binomial name, of which the first word, capitalized, is the genus and the second word is the specific epithet.
EDIT: perhaps it would further your understanding to know that in the above example, the specific epithet is latifolia. I can give you a list of 64 different species of wood, all of which have the specific epithet latifolia, and which then of necessity have different genera. I point this out to help you understand that the second word is NOT the species.
We're humans. Homo sapiens is the species name. It means 'thinking man'. This kind of terminology comes from Latin. The two words taken together make one species name. We are in the genus Homo. In the past, Homo sapiens lived at the same time other species of our genus were walking around. Homo neanderthalensis is one example. Neanderthals must have met us, because we have some DNA sequences in common - about 4% of modern Homo DNA derives from Neanderthals. So we had to have interbred at some point.
This is what the genus name implies - relationship. So, if we stepped onto a bus and sat down next to a member of the species Homo habilus we would see lots of similarities. Homo habilus is now extinct so this cannot happen.
All species names are in a form called binomial nomenclature - means two part naming system. This was invented Carl Linnaeus, a Swedish Botanist who lived in the 1700's. Back then all scientific writing was Latin, so that is why species names all seem to be backwards, because Latin grammar puts modifiers after nouns. English does not.
So - our genus is 'Homo' our specific epithet is 'sapiens'.
Separate names with a comma.