directly from the BLM
Lode Claims
Deposits subject to lode claims include, classic veins or lodes having well defined boundaries. They also include other rock in place bearing valuable minerals and may be broad zones of mineralized rock. Examples include quartz or other veins bearing gold or other metallic minerals and large volume but low grade disseminated metallic deposits. Lode claims are usually described as parallelograms with the longer side lines parallel to the vein or lode (see Figure 1). Descriptions are by metes and bounds surveys (giving length and direction of each boundary line). Federal statute limits their size to a maximum of 1,500 feet in length along the vein or lode. Their width is a maximum of 600 feet, 300 feet on either side of the centerline of the vein or lode. The end lines of the lode claim must be parallel to qualify for underground extralateral rights. Extra lateral rights involve the rights to minerals that extend at depth beyond the vertical boundaries of the claim.
Placer Claims
Mineral deposits subject to placer claims include all those deposits not subject to lode claims. Originally, these included only deposits of unconsolidated materials, such as sand and gravel, containing free gold or other minerals. By Congressional acts and judicial interpretations, many nonmetallic bedded or layered deposits, such as gypsum and high calcium limestone, are also considered placer deposits.
Placer claims, where practicable, are located by legal subdivision (for example: Township 10 South, Range 11 East, Section 9, SE1/4). The maximum size of a placer claim is 20 acres per locator (see Figure 2). An association of two locators may locate 40 acres, and three may locate 60 acres, etc. The maximum area of an association placer claim is 160 acres for eight or more persons.
The maximum size of a placer claim for corporations is 20 acres per claim. Corporations may not locate association placer claims unless they are in association with other private individuals or other corporations as co-locators.
The above came from the BLM web page.
So in answer to the question of whether it is legal to mine hard rock on a placer claim the answer is no. If you found some quartz float with gold in a river or drywash that would be fine, but if the quartz you found is part of a vein or lode, that would be hard rock. If it is part of a vein then by all means stake a claim. A lot of folks I know cover themselves by filing both types of claims over a given area so that they can mine from the lode as well as the surrounding creeks or drywashes.